Suppose the observer stands 500 feet away from the searchlight and has an angle of elevation 77∘.What is the height of the cloud cover?

Question

I keep getting 3465.18 so I am not sure what I did wrong.

Answer 1

The best thing to do is draw a picture of your situation. You have a triangle with 500 feet at the base between the observer and the cloud cover. Let's call that a y variable. Let's label x as the height of the cloud cover, which is also the height of the triangle. The hypotenuse connects the top of the cloud cover to the observer.

Since your angle of elevation is the angle of the observer looking up to the top, and we want to find the height of x, we want to use tan. So, tan(angle of elevation) = opposite(x) / adjacent(y)

Therefore...

tan(77) = x/500

tan(77) (500) = x

4.3315 (500) = x

2165.7379 = x

The height of the cloud cover is 2165.7379 feet tall.