Question

The top of the cliff is 142 m above sea level. Currently the boat is 100 metres from the buoy and the angle of depression from the top of the cliff to the boat is 64º. Find , the horizontal distance currently between the base of the cliff and the boat. diagram not to scale Top of cliff 142 boat buoy Base of cliff 1 (sea level) 100 meters. X = Х (no answer)​

Answer 1

Answer:

x = 69.30 m

Step-by-step explanation:

By the alternate angle principle, the value of angle of depression from the top of the cliff to the boat is equal to the angle of elevation from the boat to the top of the cliff (i.e 64º).

Let the horizontal distance between the base of the cliff and the boat be represented by x. Applying the appropriate trigonometric function, we have;

Tan θ = $\frac{opposite}{adjacent}$

Tan 64º = $\frac{142}{x}$

2.0503 = $\frac{142}{x}$

x = $\frac{142}{2.0503}$

x = 69.2582

x = 69.30 m

The horizontal distance between the base of the cliff and the boat is 69.30 m.