Question

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?

Answer 1

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`