Question

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

Answer 1

The answer woudl be d

Answer 2

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.