A person whose eye level is 20 feet above the ground is looking at a building. The angle of elevation to the top of the building is 31º and the angle of depression to the bottom of the building is 24∘. What is the height (in feet) of the building? Round your answer to the nearest foot.

Distance of the person from the building (x)

tan 24 = 20/x => x = 20/tan 24 = 44.92 ft

The height of the building above the height of the person and the distance of the person from the building forms two legs of right angled triangle.

Therefore, if h is the height of the building, then;
tan 31 = (h-20)/44.92
h-20 = 44.92 tan 31
h = (44.92 tan 31) + 20 = 26.99 + 20 = 46.99 ft

Answer Link

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-19T16:05:00+02:00

The height of the building with the angle of elevation as 31º and angle of depression as 24°of top and bottom of the building respectively is 46.99 ft.

What is the tangent of an angle?

The tangent of an angle is the ratio of the opposite side to the adjacent side.

Find the attached diagram to visualize it better.

[tex]tan 24=\frac{20}{x}[/tex]

[tex]x=\frac{20}{tan24}[/tex]

[tex]x=44.92[/tex]ft

[tex]tan31=\frac{y}{x}[/tex]

[tex]tan31=\frac{y}{44.92}[/tex]

[tex]y=26.99[/tex]ft

So, the height of the building = height of the eye level from the ground + y

The height of the building = 20+26.99 = 46.99 ft

Hence, the height of the building is 46.99 ft.

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