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

Answer:

Distance: 435.9 ft

Step-by-step 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,

$sin(angle)=\frac{opposite}{hypotenuse}$

Thus we can write:

$sin(35)=\frac{250}{x}$

Cross multiplying and solving for $x$ gives us:

$sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9$

Second answer choice is right: 435.9 ft