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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