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A building in a downtown business area casts a shadow that measures 88 meters along the ground. The straight-line distance from the top of the building to the end of the shadow it creates is at a 32° angle with the ground. What is the approximate height of the building? Round your answer to the nearest meter.

Respuesta :

it would be about 55 meters
JeanaShupp

Answer: 55 meters

Step-by-step explanation:

Let the height of the building be 'h'.

Since building is standing vertical to the ground making right angle.

Then , the triangle formed is a right triangle .

The given angle of elevation : [tex]32^{\circ}[/tex]

Using trigonometry , we have

[tex]\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\tan(32^{\circ})=\dfrac{h}{88}\\\\\Rightarrow\ 0.6248693519=\dfrac{h}{88}\\\\\Rightarrow\ h=0.6248693519\times88=54.988502967\approx55\text{ meters}[/tex]

Hence, the approximate height of the building = 55 meters

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