Angle of elevation and depression problems with solutions and drawing Jun 16, 2025 · Revision notes on Angles of Elevation & Depression for the Cambridge (CIE) IGCSE Maths syllabus, written by the Maths experts at Save My Exams. The angle of depression between the ranger's line of sight and the horizontal is 22°. This document outlines a learning module on angles of elevation and depression that was created by Richard B. Includes examples and practice problems. Nov 12, 2025 · Comprehensive Class 10 CBSE notes on applications of trigonometry covering angle of elevation, depression, heights and distances with solved examples, formulas, and step-by-step solutions for exam preparation. Find the height of the tree. 5 m from the horizontal level of sight. . Timestamps:00:00 Intro0:13 What i To find questions 1 to 3, please visit the page " Trigonometry Word Problems with Angle of Depression" Practice Questions Question 1 : An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. Crucially, these two angles are always equal when considering the same object and the horizontal line. It is defined as an angle between the horizontal plane and oblique line from the observer’s eye to some object above his eye. Oct 13, 2022 · Geometry Worksheet 8. Learn what angle of depression means in Maths with definition, clear formula, diagrams, and step-by-step solutions to tricky problems. As the name itself suggests, the angle of elevation is so formed that it is above the observer’s eye. 6003) Solution : Jun 16, 2025 · Revision notes on Angles of Elevation & Depression for the Cambridge (CIE) IGCSE International Maths syllabus, written by the Maths experts at Save My Exams. Exercise 14 Some students may think the angle of depression is the angle between the vertical segment to the ground and the ship. Explore how trigonometric ratios relate angles to the sides of a right triangle. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. It defines angles of elevation and depression, provides step-by-step methods for finding these angles, and includes several examples and problems with solutions. The opposite of the angle of elevation is the angle of depression which is formed when an observer looks downwards. After this lesson, we expect you to learn the concepts of the angle of depression and be able to confidently explain what it is. Aug 19, 2023 · Angle Of Elevation And Depression Word Problems Worksheet With Answers – Angle worksheets are a great way to teach geometry, especially to children. These worksheets include 10 types of questions about angles. Electronic instruments on a treasure-hunting ship detect a large object on the sea floor. How tall is the office building? 500 ________9. Draw a diagram for ea. Master this concept for exams with easy examples and expert tips. Angles of elevation and depression are commonly found in real-world scenarios, such as measuring the height of a building or the distance to a ship at sea. Find the height of the pole. An angle of depression is an angle that comes down from the horizontal. F. (Some are started for you). Word problems involving angles of elevation and depression, straight object leaning against a vertical object, etc, are usually modeled using right triangles. In this explainer, we will learn how to solve real-world problems that involve angles of elevation and depression using the tangent ratio. Eventually, this angle is formed above the surface. The angle from the top of the shorter building to the top of the taller building is 20 . And if the line of sight is above the horizontal line, then the angle is called the angle of elevation. Learn to solve angle of elevation and depression problems with this precalculus lesson. Angles of elevation and depression Starter 1. 26K subscribers 9. The angle of elevation depends upon the movement of your eyes. Given that the plane’s elevation is 2400 m, determine the distance between the two fires. Jul 11, 2024 · A comprehensive guide to understanding and applying angles of elevation and depression in geometry. Find how far the ladder is from the foot of Jan 11, 2023 · Learn the angles of elevation and depression. 4 Remember also solving for angles with trig? 5 Now let's do some word problems!!! Write down the definitions as notes. MATH 9 Q4 Module 3-4 Illustrating Angle of Elevation and Angle of Depression - Free download as PDF File (. The building is 30 ft tall. In this article, we will discuss the 'Angle of Elevation' in detail. Example 1 : A student sitting in a classroom sees a picture on the black board at a height of 1. If the yacht is 1. This angle is formed above the horizontal line. Learn how to solve problems involving angles of elevation and depression with detailed explanations, examples, and tips for Cambridge IGCSE Mathematics. What is the angle of elevation and what is the angle of depression, How to find the angle of elevation and depression using trigonometry, How to solve word problems that involve angle of elevation and depression, in video lessons with examples and step-by-step solutions. You can use your knowledge of the angle of elevation and depression and the six trigonometric functions to calculate unknown distances. The base of the cliff is at sea level. To the nearest foot, how high is the building? Feb 24, 2012 · Very frequently, angles of depression and elevation are used in these types of problems. Explore the angles of elevation and depression through real-life examples, highlighting their crucial roles in architecture, aviation, and everyday applications. In the diagram, ∠2 is the angle of depression. From an airplane at an altitude (height) of 1200 m, the angle of depression to a rock on the ground measures 28°. Problem 1 : From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. For lengths, answer to 1 decimal place. The following diagram clarifies the difference between an angle of depression (an angle that looks downward; relevant to our problem) and the angle of elevation (an angle that looks upward; relevant to other problems, but not this specific one. Improve your understanding of trigonometry by solving real-life scenarios involving heights, distances, and angles. He finds that the angle of elevation of the top of the tree is 38° and the angle of depression of its reflection in the water is 56°. This document contains a worksheet with 12 problems involving trigonometric calculations of angles of elevation and depression. angle of elevation, angle of depression, trigonometry worksheet, height and distance problems, right triangle, elevation angle Jul 3, 2023 · Angle of Depression is one of the two important angles in Trigonometry, the other being the angle of elevation. Find how far the ladder is from the foot of Angle of Elevation of point A from another point B below refers to the angle between the horizontal from point B and the line of sight from point B to point A. It is the angle formed between the horizontal line which is straight to the observer's eye and the line of sight. Practice applying these concepts to solve real-world problems involving heights, distances, and angles. In the diagram on the right, the angle A is the angle of elevation of the base of the lighthouse from the yacht . Draw your own picture and then use sohcahtoa to solve for the missing information!!! In this video, we will learn how to solve real-world problems that involve angles of elevation and depression. Learn how to apply angles of depression and elevation to real-world problems. Dec 28, 2024 · Learn the definition of elevation and depression, their formulas, and some facts with solved examples here at Embibe. He observes that the angle of elevation of the top of a cliff is 40° and the angle of depression to the base of the cliff is 20°. The document explains the applications of trigonometry in measuring angles of elevation and depression using a theodolite, detailing the setup and use of right triangles to solve problems related to real-world scenarios. It is pretty obvious that an angle of elevation measures up and an angle of depression measures down. Make sure to round off your final answer to 2 decimal places. Maths Book back answers and solution for Exercise questions - Mathematics : Trigonometry: Problems involving Angle of Elevation and Depression: Exercise Problem Questions with Answer Exercise 6. Jul 31, 2020 · Create a real-life scenario involving an angle of elevation or depression. Scroll down the page for more examples and solutions on solving problems with angle of elevation or angle of depression. The angle your line of sight makes with the horizontal line is the angle of elevation. This page includes step-by-step solutions to practice problems that help you visualize and solve each scenario. Q1. The following figures show some examples of angle of elevation and angle of depression. If you look downwards, the angle relative to the horizontal line is called an angle of depression. 8 meters tall and can be measured using a clinometer or theodolite. It is a concept that we come across in trigonometry and can be used to find the height of buildings, mountains and other such figures. How high above the ground is the kite flying? 2. For angles, answer to the nearest minute. The angle of elevation is the angle between the horizontal line of sight and the line of sight up to an object. Let's look at some practice problems that will help you understand how to do this. The angle of elevation for the top of the office building is 23 and the angle of depression for the base of the building is 50 . 4 1. (these go along with pages 11-12 in your Ch 8 Packet if you have it with you still) An angle of elevation is an angle that comes up from the horizontal. Understand the concepts of angle of elevation and depression in trigonometry. Angle of elevation Angle of depression Cliffs Similarly, if you look down at something, then the angle between your line of sight and the horizontal is called the angle of depression. Ask each student to draw a diagram that represents the situation in the exercise and then compare diagrams with a partner. As the picture is not clear to him, he moves straight towards the black board and sees the picture at an angle of elevation of 45°. h question. This trigonometry video tutorial explains how to solve angle of elevation and depression word problems. Step 5: Draw a point below the horizontal line to represent an object at a lower elevation. Conversely, if you're looking down at an object below your horizontal line, the angle formed is the angle of depression. Jan 20, 2017 · Using trigonometry to find angles of elevation or depression The document explains the concepts of angles of elevation and depression, including their definitions, applications in real-life situations, and methods for solving related problems. from a point 20m from its ba. Word problems involving ang MATH 9 Q4 Module 3-4 Illustrating Angle of Elevation and Angle of Depression - Free download as PDF File (. Mar 24, 2025 · Step 4: Mark the angle between the horizontal line and the line of sight to the elevated object as the angle of elevation. From the top pf a cliff 300 feet high, the angle of depression of a boat measure 45 ̊, how far is the boat from the cliff? 2. The pilot of an airplane flying at 20,000 feet sees the angle of depression to the airport is 30 ̊, how far (horizontally) is the plane from the airport? 3. Get angle of elevation and depression word problems with answers in PDF format. Find the height of the building. It outlines the steps for problem-solving, the importance of these angles in fields like physics and environmental science, and provides examples for understanding and calculating these angles. The angle of elevation is a widely used concept related to height and distance, especially in trigonometry. In this lesson, we will learn how to solve real-world problems that involve angles of elevation and depression using the tangent ratio. Sep 21, 2024 · The elevation angle is formed when it is between the line of sight and the horizontal line. Learn how to find the distance between 2 ships using the angle of depression. In this explainer, we will learn how to solve real-world problems that involve angles of elevation and depression. Notes Angles of elevation and depression are always measured from the horizontal. A word problem is a real-life situation which can be modelled mathematically. 732) Solution (5) From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. 5 Angles Of Elevation And Depression Answers – Angle worksheets are a great way to teach geometry, especially to children. The angle of depression is formed when an observer looks down at an object. Nov 1, 2025 · Real-World Applications of angle of elevation and angle of depression. 732) Solution : Angle of elevation and depression. One of the keys to being a good problem solver is to draw a picture using all the data given. The module is designed to illustrate What is the angle of depression from the top of the building to the car? Give your answer to the nearest degree. It covers right triangle trigonometry topics on how Trig Word Problems – Angles of Elevation and Depression 1. The angle of elevation of an object is its angular height (in degrees) above a reference line. Angle of Elevation & Depression Trig Worksheet *Draw and label a picture for each problem 1. Word Problems Angles of Elevation and Depression 1) A woman is standing on the ground at a point 78ft from the base of a building. How are has it travelled (a) west (b) south? Give your answers to the nearest kilometre. The angle of depression from to a boat at is È . The fire to the west is found at an angle of depression of 38°. Solve quantitative aptitude problems related to angles of elevation and depression. What is the angle of elevation of the top from a point on the ground 7 ft from the base of the building? A ladder leaning against a wall makes an angle of 65° with the ground. Find the distance between the two boats. If the foot Problems Problem 1 : From the top of a rock 50 √ 3 m high, the angle of depression of a car on the ground is observed to be 30°. The three general words associated with the angle of elevation are angles, horizontal lines, and line of sight. In the angle of depression, the line of sight is downwards to the horizontal line. If the angle goes "downwards" it is called an angle of depression. The angle of depression of an object is its angular ‘depth’ (in degrees) below a reference line. The module includes a PowerPoint presentation, additional activities, outputs from two classes (Goldfish and Grouper), an analysis of results from the Goldfish class, and discussions of challenges encountered and solutions implemented. The application of the angle of elevation and depression through the sample problems is Jun 16, 2025 · Revision notes on Angles of Elevation & Depression for the Cambridge (CIE) O Level Maths syllabus, written by the Maths experts at Save My Exams. If the angle of elevation to the kite measures 70°, and Brian is holding the kite 1. nute. Nov 14, 2025 · This lesson note on angles of elevation and depression for JSS 2 explains identifying, distinguishing, measuring angles, and calculating distances and heights. 👉 Learn how to solve word problems with triangles. Jul 30, 2013 · Learn about angles of elevation and depression in trigonometry, their real-world applications, and how to solve related problems effectively. Solution : Angle of Elevation/Angle of Depression Problems MrD Klinkerman 6. It is important to learn about the angle of elevation and depression while studying heights and distances in trigonometry. The angle of elevation in the above diagram is α ∘ α∘. The fire to the east is found at an angle of depression of 47°. The angle from the top of the shorter building to the base of the taller building is 45 . Homework 1. What if you placed a ladder 10 feet from a haymow whose floor is 20 feet from the ground? Draw/Illustrate the given problems involving angle of elevation and angle of depression. 7km from the base of the cliff, find how high the cliff is. 2. 2 m off the ground. A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60°. Trigonometry can be used to solve problems that involve angles of elevation or depression. The distance is metres. Jun 4, 2020 · Learn about the difference between the angle of elevation and depression and how to draw it in a figure. 6003) Solution : Download Study notes - Angle of Elevation & Depression Trig Worksheet | Southwestern University (SWU) | Angle of Elevation & Depression Trig Worksheet. 732 Angles of elevation/inclination are angles above the horizontal; angles of depression/declination are angles below the horizontal. Draw a diagram for each question. We will also look at solved examples and practice problems on the concept of angle of elevation. One of the most common applications of right triangle trigonometry in the real-world are angles of elevation and depression word problems. pdf), Text File (. Find the height of the tower and the width of the canal. Learn their definitions, real-world applications, problem-solving strategies, and practical uses in various fields. Solving real-life problems involving right triangles requires knowledge of some significant terms such as line of sight, angle of elevation, and angle of depression. If the object is below the level of the observer, then Jun 16, 2025 · Revision notes on Angles of Elevation & Depression for the Cambridge (CIE) IGCSE International Maths syllabus, written by the Maths experts at Save My Exams. Paulino. 2K Use angles of elevation and depression to calculate distances and heights using scale drawing. Angle of depression is defined as the angle formed by the horizontal line and the downward line of Sep 14, 2025 · To find the angle of elevation and depression, draw a sketch of the situation, mark in the given angle of elevation or depression, and use trigonometry to find the required missing angle or length. Nov 21, 2023 · Learn about angles of elevation and depression with clear explanations in just 5 minutes. Brian’s kite is flying above a field at the end of 65 m of string. These types of problems are famous for requiring the use of trigonometric ratios to relate a given angle and side length to find an unknown side length. Q1 The angle of elevation of the top of a flag pole. For example, a man is 1. This point will be used to illustrate the angle of depression. The angle of depression refers to the angle at which one must look downward from a horizontal position to view an object situated at a lower level. It is the angle that the bird would lower (or depress) its line of sight from the horizontal to see the bird watcher. Apr 8, 2024 · II. For Learn how to work with angle of elevation and depression problems in this free math video tutorial by Mario's Math Tutoring. Angle of Elevation: The angle measured up from the horizon or a horizontal line. The problems apply trigonometric concepts like tangent, opposite/adjacent ratios to determine unknown distances or heights given known angles of elevation/depression and one other piece of distance information for each scenario. Show your complete solution. In this video, I go through an angle of elevation and depression word problem. You can use trigonometry to find the angle of elevation and the angle of The angle of elevation of the top of the tower is 58°. Find the distance of the car from the rock. The angle of elevation of the picture is 30°. From the top of a cliff 88 m above the canyon floor, the angle of depression to the edge of the river is 37°. The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. (Review of last lesson) A ship sails 250 km on a bearing of 238∘ . Find the distance from the plane to the rock. ∠ABO = ∠O = θ Angle of Depression Problems Example 1: When working with angles of elevation and depression, drawing clear and precise diagrams can significantly aid in problem visualization and solution formulation. This video lesson provides examples and an optional quiz for practice. Find the height of the second tree. In the diagram on the right, the boat makes an In this lesson, we will learn how to solve real-world problems that involve angles of elevation and depression. Angle of Depression and Angle of Elevation are equal become they are The angle of depression is basically the measure of an angle between the horizontal line and line of sight of a person’s eyes to any item below. Whenever you have one of these angles, you should immediately start picturing how a right triangle will fit into the description. We go through a typical word problem encountered when students are learning about angle of depression involving right Get these free trigonometric word problems worksheets to better understand how to approach these problems. Click to know more about the angle of depression! Angles of Elevation and Angles of Depression Word Problems Angles of elevation and angles of depression word problems are some of the most common problems in studies of trigonometry. Master the concept of Angle of Elevation and Depression with our step-by-step revision notes. MathBitsNotebook Geometry Lessons and Practice is a free site for students (and teachers) studying high school level geometry. Additionally Draw and label a picture for each problem. From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. When you look upwards or downwards, you can measure an angle relative to an imaginary horizontal line. In order to solve problems involving angles of elevation or depression, we need to be able to determine which angle in the problem refers to an elevation or depression. Background Information for Learners This learning activity sheet is about illustrating angles of elevation and depression. Solution : In this section, we try to solve problems when Angles of depression are given. Q1 The angle of elevation of the top of a flag pole from a point 20m from its base is 32°. Now, prior to looking at examples and recalling trigonometric ratios and the laws of sines and cosines, we In this explainer, we will learn how to solve real-world problems that involve angles of elevation and depression using the tangent ratio. An angle of depression is the angle formed by a horizontal line and a line of sight to a point below. The lesson This document contains 7 problems involving calculating distances and angles of elevation/depression. (tan 58° = 1. Use trigonometry to find the distance from the base of the tower to the fire. ) 2 days ago · Before jumping to the word problems, here are the basic definitions you need to be familiar with: The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (also known as the line of sight). From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the angle of elevation to the bottom of the sign are 40° and 32°, respectively. Jul 23, 2025 · The concept of angle of elevation holds fundamental significance in trigonometry and has diverse practical applications across different fields. Before you start with this explainer, you should be confident finding angle measures and missing sides using right triangle trigonometry and the laws of sines and cosines. These will help you easily understand angle of elevation. The angle of elevation is the "upwards" angle from the horizontal to a line of sight from the observer to some point of interest. As learners navigate through these problems, they not only master the angles of elevation and depression but also enhance their analytical capabilities—an achievement that resonates well beyond the classroom. That’s why I put together the best angles of elevation and depression word problems worksheet that you will ever find! Angles of Elevation and Depression 8271. Angle of Depression: The angle measured down from the horizon or a horizontal line. See examples and practice problems from everyday life of the angle of depression and the angle of elevation. (√ 3 = 1. From the foot of a building, I have to look upwards at an angle of 22 degrees to see the top of a tree. If you look upwards, the angle relative to the horizontal line is called an angle of elevation. txt) or read online for free. Draw an appropriate diagram and explain how to solve your example. The boat heads towards the base of the cliff, , and stops at . Emphasize that one side of an angle of depression or of an angle of elevation must be horizontal. (2 marks) The base of a lighthouse, , is at the top of a cliff metres above sea level. The angle of elevation to the top of the building is 57 . Enhance learning with online and unlimited homework assistance. r angles, answer to the nearest m. *Draw and label a picture for each problem. The angle of elevation from a yacht to the top of a cliff is 18o. Jan 21, 2020 · Angles of Elevation and Depression help us find distances between things like Radar Stations to Planes, Lighthouses to Buoys; two boats at sea and more. Aug 8, 2025 · Before you even think about numbers or formulas, the single most critical step in solving any problem involving angles of elevation or depression is to draw an accurate diagram. 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