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A man on the fifth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street?

Verified Answer :

klm747klm747

The answer is about 57 feet.

JeanaShupp

Answer: 57 feet


Step-by-step explanation:

Given: The angle of elevation from the street to the man in the building=\(35^{\circ}\)

If the man in the building is 40 feet up.

From the given , we make a diagram in which \(\triangle {ABC}\) is a right triangle, such that

Let AB=40 feet

Then \(\tan{35^{\circ}}=\frac{AB}{BC}\)

\(\\\Rightarrow0.70=\frac{40}{BC}\\\\\Rightarrow\ BC=\frac{BC}{0.70}=57.142\approx57\ feet\)

Hence, the distance of the person on the street  from the building is 57 feet

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