Question

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

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

Answer 1

104.82 ft

Explanation:

A P E X

Answer 2

Answer: A. 104.82 feet

Explanation:

You can observe in the figure a right triangle, where the height of the building is "x".

You need to use the identity:

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

You can identify in the figure that:

`opposite=x\\adjacent=2,000\\\alpha=3\°`

Then, you can substitute these values into
`tan\alpha=(opposite)/(adjacent)`:

`tan(3\°)=(x)/(2,000)`

Solve for x:

`x=(2,000)(tan(3\°)\\x=104.815`

Therefore, the height of the building to the nearest hundredth foot is:

104.82 feet