Question

determine the height of each triangle. round to the nearest foot. a. 7 ft b. 5 ft c. 8 ft d. 4 ft

Explanation:

Step1: Use sine function

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 60^{\circ}$ and the hypotenuse is 8 ft, and the height $h$ is the side opposite the $60^{\circ}$ angle. So $\sin60^{\circ}=\frac{h}{8}$.

Step2: Recall sine - value

Since $\sin60^{\circ}=\frac{\sqrt{3}}{2}$, we have the equation $\frac{\sqrt{3}}{2}=\frac{h}{8}$.

Step3: Solve for $h$

Cross - multiply to get $h = 8\times\sin60^{\circ}=8\times\frac{\sqrt{3}}{2}=4\sqrt{3}\approx4\times1.732 = 6.928\approx7$ ft.

Answer:

A. 7 ft