An observer stands on the ground and looks up a... - JSS3 Mathematics Trigonometric Ratios Question

An observer stands on the ground and looks up at an angle of elevation of 25 degrees to see the top of a tower. If the tower is 50 meters tall, how far is the observer from the base of the tower?

Given:

Angle of elevation (θ) = 25 degrees

Height of the tower (opposite side, opp) = 50 meters

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

tan(25∘)=50/adj

adj=50

tan(25∘)50

Using a calculator:

tan(25∘)≈0.4663

adj≈ 0.4663/50=107.19 meters

So, the observer is approximately 107.19 meters away from the base of the tower.

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