Question

the measurement from the base of a tree to the tip of its shadow is 100 ft. the angle of inclination is 60°. given: sin 60° = 0.866, cos 60° = 0.5, tan 60° = 1.732. *not drawn to scale. how tall is the tree? a. 50 ft b. 86.6 ft c. 115.5 ft d. 173.2 ft e. 200 ft

Explanation:

Step1: Identify trig - ratio

We know the adjacent side to the angle ($x = 100$ ft) and we want to find the opposite side ($y$) of the right - triangle. The tangent function is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Apply the tangent formula

Given $\theta = 60^{\circ}$, $\tan60^{\circ}=1.732$, and adjacent side $a = 100$ ft. Using $\tan\theta=\frac{y}{a}$, we substitute the values: $y=a\times\tan\theta$.
$y = 100\times\tan60^{\circ}$.

Step3: Calculate the height of the tree

$y=100\times1.732 = 173.2$ ft.

Answer:

D. 173.2 ft