Question

what is the height of the building shown below? round to the nearest tenth if necessary. 100 ft 51° h 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 hypotenuse is 100 ft, and the height of the building $h$ is the opposite - side. 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