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

Answer:

$184.38\ ft$

Step-by-step 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

Answer 2

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.