Angle of Elevation and Depression: O-Level Math Guide
This revision note extends your trigonometry knowledge to angles of elevation and depression. These concepts help calculate the heights and distances of objects from your line of sight
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What is the Angle of Elevation?
The angle of elevation is the upward angle formed between the horizontal ground and your line of vision when observing an object above you. This angle is measured from the horizontal plane upward to the object.
What is the Angle of Depression?
The angle of depression is the downward angle formed between the imaginary horizontal ground and your line of vision when observing an object below you. This angle is measured from the horizontal plane downward to the object.
Important Tips to Find Angle of Elevation and Depression
Always measure the angles from the horizontal line.
As they are alternate angles, the angle of elevation is always equal to the angle of depression.
Steps to Find Angle of Elevation and Depression
Step 1: 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 is 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, measured from his eye level?
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.
Solution:
(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)
Last Minute Revision for O Level Math?
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