Question

HELP ASAP PLEASE

The area of elevation to the top of a 10-story skyscraper is measured to be 3° from a point on the ground 2,000 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?

A. 285.09 feet
B. 66.58 feet
C. 104.67 feet
D. 104.82 feet

Answer 1

I believe it's D, 104.82 feet.

Answer 2

Hello!

Let's think of this scenario as a triangle. This 3 degree angle is opposite from the building, and the adjacent side to this angle is 2,000 feet. We know that the tangent deals with opposite and adjacent side. Let's find it below.

tan3≈0.052

This gives us the equation below.

x/2,000=0.052

Now we solve. Let's multiply each side by 2,000.

x=104

As you can see, 104 is very close to both C and D. Instead of using 0.052, let's just use the exact tangent of 3. We multiply this by 2,000. By doing so, we get about 104.82.

Therefore, our answer is D) 104.82

I hope this helps!