A lighthouse is 33 m above sea level. The angle of depression to a small fishing boat is 24 degrees. How many meters is the fishing boat from the cliff?

Question

A lighthouse is 33 m above sea level. The angle of depression to a small fishing boat is 24 degrees. How many meters is the fishing boat from the cliff?

Answer 1

Form a right triangle of height h and base b.

 

h = 33 m

b = distance to boat = ?

θ = angle of depression = 24°

 

From basic trigonometry,

 

tanθ = h/b ⇒

 

b = h/tanθ = (33 m)/tan24° ≅ 74.1 m