Question

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

A. 174.39 feet
B. 174.82 feet
C. 83.13 feet
D. 96.49 feet

Answer 1

The point of observation is 2500 m away from the foot of the building.

The angle of elevation is 4°.

We need to find the height 'h' of the building.

With respect to 4°,

2500 is the adjacent side.

'h' is the opposite side.

The trigonometric ratio associating opposite & adjacent is tan.

We have

`tan\theta =(opposite)/(adjacent)`

`tan4^(o)=(h)/(2500)`

Cross multiplying we get

h = 2500 tan4°

h= 174.82 m

Option B) is the right answer.