Question

question 6 of 26 a tree casts a shadow that is 20 feet in length. if the angle of elevation is 32°, which of the following best represents the height of the tree? a. 10.5 ft b. 9.5 ft c. 12.5 ft d. 11.5 ft

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the shadow length is the adjacent side ($a = 20$ ft) to the angle of elevation ($\theta = 32^\circ$), and the height of the tree ($h$) is the opposite side. We use the tangent function: $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{h}{20}$.

Step2: Solve for $h$

Rearrange the formula: $h = 20\times\tan(32^\circ)$. Calculate $\tan(32^\circ)\approx0.6249$. Then $h\approx20\times0.6249 = 12.498\approx12.5$ ft.

Answer:

C. 12.5 ft