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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?

Respuesta :

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.
calculista

Answer:

[tex]184.38\ ft[/tex]

Step-by-step explanation:

we know that

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

In this problem we have

[tex]\theta=2\°[/tex]

[tex]adjacent\ side=5,280\ ft[/tex]

Let

h-----> the opposite side to the angle [tex]\theta[/tex] (represent the height)

so

[tex]tan(2\°)=h/5,280[/tex]

[tex]h=5,280*tan(2\°)=184.38\ ft[/tex]

see the attached figure to better understand the problem


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