Question

A ship has a 15-foot-tall mast with a 37.13-foot-long rope that is strung from the top of the mast to the ship's deck. What is the angle of elevation to the top of the mast?

Answer 1

The angle of elevation to the top of the mast is 23.82°

Explanation:

Given as :

The length of the rope = 37.13 foot

The length of the mast = 15 foot

Let the angle of elevation to the top of the mast = Ф

So, Sin angle =
`(\textrm perpendicular)/(\testrm hypotenuse)`

Or, Sin Ф =
`(\textrm length of mast)/(\testrm length of rope)`

or, Sin Ф =
`(\textrm 15)/(\testrm 37.13)`

or , Sin Ф = 0.40398

∴ Ф =
`Sin^(-1)` 0.40398

or, Ф = 23.82°

Hence The angle of elevation to the top of the mast is 23.82° Answer