Question

A surveyor standing on top of a cliff found that the angle of depression of a boat as sea is 22°. if the top of the cliff is 15m above sea level how far is the boat from the foot of the cliff?​

Answer 1

From the photo above i interpreted the question and drew a triangle to make it easier to solve

Tan is used to solve the question as we were given opposite (as height of the cliff) and to find Adjacent ( the distance between the foot of the cliff to the boat)

Tan θ =Opp/Adj

Tan 22°=15/a

Cross Multiply

aTanθ=15°

Divide both sides by Tan 22

aTan22/Tan22 = 15/Tan 22

a = 15/Tan 22°

a = 37.13 m

Therefore the distance between the foot of the cliff to the boat is 37.13 metres