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solniwko [45]
3 years ago
5

A tree casts a shadow that is 20 feet in length. if the angle of elevation is 32 degrees, which of the following best represents

the height of the tree?
A. 10.5 FT
B. 9.5 FT
C. 11.5 FT
D. 12.5 FT

Mathematics
2 answers:
swat323 years ago
7 0
The answer woudl be d

34kurt3 years ago
7 0

Answer: D. 12.5 FT

Step-by-step explanation:

Let the height of tree be x.

Assume tree is standing vertical to the ground, then it will make right triangle with the shadow of the tree.

Given: The length of the shadow: 20 feet

Using trigonometry,

\tan\thetha=\dfrac{\text{side opposite to }\theta}{\text{Side adjacent to }theta}\\\\\Rightarrow\ \tan32^{\circ}=\dfrac{x}{20}\\\\\Rightarrow\ x=\tan32^{\circ}\times20\\\\\Rightarrow\ x=0.6248693519\times20\\\\\Rightarrow\ x=12.497387038\approx12.5\ ft.

Hence, the height of tree= 12.5 ft.

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