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 the trig - ratio

We know the adjacent side (length of shadow = 100 ft) to the given angle ($60^{\circ}$) and we want to find the opposite side (height of the tree). We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan60^{\circ}=\frac{h}{100}$, where $h$ is the height of the tree.

Step2: Solve for the height

Given $\tan60^{\circ}=1.732$, we can rewrite the equation as $1.732=\frac{h}{100}$.
Multiply both sides by 100: $h = 1.732\times100$.
$h = 173.2$ ft.

Answer:

D. 173.2 ft