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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?

Verified Answer :

meerkat18

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.

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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


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