Question

a sailor sights the top of a 200-foot cliff at a 17 degree angle of depression. how far is the boat from the base of the cliff​

Answer 1

The boat is roughly 654ft away from the base of the cliff.

Explanation:

We have the angle 17°

The side opposite the angle is 200ft.

We want to find the length of the adjacent side.

So what equation has Opposite and Adjacent in it?

Tangent. (Remember SOH-CAH-TOA)

Tan = opp/adj

Tan(theta°) = opp/adj

Rearranging,

adj = opp/tan(theta°)

adj = 200/tan(17°)

adj = 654.17ft

And to double check you answer,

° = tan^-1(opp/adj)

° = tan%-1(200/654)

° = 17°