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An observer stands on top of a hill and looks d... - JSS3 Mathematics Trigonometric Ratios Question

An observer stands on top of a hill and looks down at an angle of depression of 20 degrees to see a road directly below. If the height of the hill is 60 meters, how far is the road from the base of the hill?

Given:

Height of the hill (opposite side, opp) = 60 meters

Angle of depression (θ) = 20 degrees

To find the horizontal distance (adjacent side, adj):

tan(20∘)=60adj

adj=60

tan(20∘)

adj= tan(20 ∘ )60

 

Using a calculator:

tan(20∘ )≈0.3640

adj≈60/0.3640=164.84 meters

So, the road is approximately 164.84 meters away from the base of the hill.

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