Question

The angle of elevation to the top of a 15-story skyscraper is measured to be 4 degrees from a point on the ground 2,500 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?

A. 83.13 feet
B. 174. 82 feet
C. 96.49 feet
174. 39 feet

Answer 1

Set up a right triangle
The base will be 2,500 feet and the angle where the hypotenuse meets the base will be 4 degrees
The height is your x value,
tan4=x/2,500
Multiply both sides by 2500
2500tan4=x
x=174.817
The answer is B

Answer 2

Option B
`174.82\ ft`

Explanation:

we know that

In the right triangle ABC

`tan(A)=(BC)/(AC)`

see the attached figure to better understand the problem

we have that

`A=4\°`

`AC=2,500\ ft`

`BC=h\ ft` ----> is the height of the skyscraper

substitute and solve for h

`tan(4\°)=(h)/(2,500)`

`h=2,500*tan(4\°)=174.82\ ft`