Question

red maple trees can reach heights of up to 80 feet. what is the height of the maple tree shown below? round to the nearest tenth if necessary.
95 ft
35°

a. 66.5 feet
b. 109.3 feet
c. 54.5 feet
d. 77.8 feet

Explanation:

Step1: Identify the trigonometric relation

We know that in a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 35^{\circ}$ and the hypotenuse is 95 ft, and the height of the tree $h$ is the opposite side to the angle $\theta$.
So, $\sin35^{\circ}=\frac{h}{95}$.

Step2: Solve for $h$

We can rewrite the equation as $h = 95\times\sin35^{\circ}$.
Since $\sin35^{\circ}\approx0.5736$, then $h=95\times0.5736 = 54.492\approx54.5$ ft.

Answer:

C. 54.5 feet