michaelmiller3
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A building that is 100 ft tall casts a shadow that makes a 30 degree angle with the ground. Approximately how long, in feet, is the shadow across the ground?

Verified Answer :

foggles

If the height of the building is 100 ft, and the angle made with the ground is 30°:
You can say that tan(30) = 100/x
Rearranging for x you get x = 173.2 ft

Answer: The length of the shadow is 173.2 feet long

Step-by-step explanation:

Since we have given that

Length of a building = 100 feet

Angle of elevation that a shadow makes with the ground = 30°

We need to find the length of the shadow :

We will use "Trigonometric Ratios: :

\(\frac{AB}{BC}=\tan 30\textdegree\\\\\frac{100}{BC}=\frac{1}{\sqrt{3}}\\\\BC=100\times \sqrt{3}\\\\BC=100\times 1.732=173.2\ feet\)

Hence, the length of the shadow is 173.2 feet long .

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