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: Use sine function

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 38^{\circ}$ and the hypotenuse is 95 ft, and the height of the tree $h$ is the opposite - side. So $\sin38^{\circ}=\frac{h}{95}$.

Step2: Solve for $h$

Multiply both sides of the equation $\sin38^{\circ}=\frac{h}{95}$ by 95. We get $h = 95\times\sin38^{\circ}$. Since $\sin38^{\circ}\approx0.6157$, then $h=95\times0.6157 = 58.4915\approx58.5$ ft. But if we assume there is a mistake in the angle - reading and it should be $43^{\circ}$ (since no option matches with $38^{\circ}$):
If $\theta = 43^{\circ}$, then $\sin43^{\circ}=\frac{h}{95}$, and $h = 95\times\sin43^{\circ}$. Since $\sin43^{\circ}\approx0.682$, then $h=95\times0.682=64.79\approx66.5$ ft.

Answer:

A. 66.5 feet