Question

value: 2
what is the height of the building shown below? round to the nearest tenth if necessary.
100 ft
51°

a. 62.9 feet
b. 132 feet
c. 123.5 feet
d. 77.7 feet

Explanation:

Step1: Use sine function

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 51^{\circ}$ and the hypotenuse is 100 ft, and the height $h$ of the building is the opposite - side to the angle $\theta$. So, $\sin(51^{\circ})=\frac{h}{100}$.

Step2: Solve for $h$

$h = 100\times\sin(51^{\circ})$. Since $\sin(51^{\circ})\approx0.777$, then $h=100\times0.777 = 77.7$ ft.

Answer:

d. 77.7 feet