Question

Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is 35∘ and the depth of the ocean, at that point is 250 feet. How far away is she from the reef? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Distance: 435.9 ft

Explanation:

This is a right triangle shown in the picture.

To solve for
`x`, we can use trigonometry.

The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is
`x` (what we are seeking to find).

The ratio that relates opposite and hypotenuse is sine.

We know that,

`sin(angle)=(opposite)/(hypotenuse)`

Thus we can write:

`sin(35)=(250)/(x)`

Cross multiplying and solving for
`x` gives us:

`sin(35)=(250)/(x)\\x=(250)/(sin(35))\\x=435.9`

Second answer choice is right: 435.9 ft