From the top of a lighthouse 97 feet high, the angle of depression to a small boat is 40degrees. How far from the foot of the lighthouse is the boat?

Question

asked Sep 15, 2021 33.5k views

1 Answer

Featherbelly · Answer 1 · 2021-09-21T04:41:50+0000

Answer:

Step-by-step explanation:

Given

height of light house is
$h=97\ feet$

Angle of depression
$\theta =40^(\circ)$

using Trigonometry we can write as

$\tan \theta =(Perpendicular)/(base)$

$\tan \theta =(97)/(x)$

$x=(97)/(\tan 40)$

$x=115.60\ ft$

So boat is at a distance of
$115.06\ ft$