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 (distance from base of tree to tip of shadow = 100 ft) and we want to find the opposite side (height of the tree). We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Set up the equation

Let $h$ be the height of the tree. Given $\theta = 60^{\circ}$ and adjacent side $a = 100$ ft. The formula is $\tan60^{\circ}=\frac{h}{100}$.

Step3: Solve for $h$

Since $\tan60^{\circ}=1.732$, we have $h = 100\times\tan60^{\circ}$. Substituting the value of $\tan60^{\circ}$, we get $h=100\times1.732 = 173.2$ ft.

Answer:

D. 173.2 ft