Angle of Elevation and Depression

 

In this revision note, you will learn to extend your knowledge of Trigonometry to find angle of elevation and depression.

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o level math revision notes

 

Angle of Elevation

When you look at an object above your location, the angle formed between the horizontal ground and the line of sight is called the angle of elevation.

angle of elevation

Angle of Depression

When you look at an object below your location, the angle formed between the imaginary horizontal ground and the line of sight is called the angle of depression.

angle of depression

Important Tips to Find Angle of Elevation and Depression

Always measure the angles from the horizontal line.

Angle of elevation is always equal value as angle of depression. They are alternate angles.

angle of elevation and depression

Steps to Find Angle of Elevation and Depression

Step 1: Draw a sketch of the situation.

Step 2: Mark in the given angle of elevation or depression.

Step 3: Use trigonometry to find the required missing angle or length.

Example 1 Angle of elevation

A boy flying a drone tracking its direction. The drone is 400 m away from the boy and the drone is flying at a vertical height of 250 m above the eye level. What is the angle of
elevation of the drone from the boy, measure from his eye level ?

angle of elevation example 1

Solution:

sin θ = 250/400

Angle of elevation, θ = 38.7°

Example 2 Angle of Depression

TY is a building of height 90 m. The angle of depression of a car C from the top T is 40°.
Find
(a) the value of ∠CTY.
(b) the value of ∠TCY.
(c) the distance between C and Y.

angle of depression example

Solution:

angle of depression example solutions

(a) ∠CTY = 90° – 40° = 50°

(b) ∠TCY = 40° (alt. ∠s)

(c)

tan 40° = 90/CY

CY = 90/ tan 40°

= 107.2578 (4 dp)

=107 m (3 sf)

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