Question

The angle of elevation to the top of a 30-story skyscraper is measured to be 2 degrees from a point on the ground 5,280 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?

Answer 1

we are given an angle of elevation of 2 degrees and distance in the x axis of 5280 feet and we are asked in the problem to determine the height of the building. We use the tangent function to determine the height: that is tan 2 = h / 5280; h is equal then to 184 ft.

Answer 2

`184.38\ ft`

Explanation:

we know that

In a right triangle the tangent function of an angle
`\theta` is equal to divide the opposite side to the angle
`\theta` by the adjacent side to the angle
`\theta`

In this problem we have

`\theta=2\°`

`adjacent\ side=5,280\ ft`

Let

h-----> the opposite side to the angle
`\theta` (represent the height)

so

`tan(2\°)=h/5,280`

`h=5,280*tan(2\°)=184.38\ ft`

see the attached figure to better understand the problem