Question

determine the height of the triangle. round to the nearest foot. a. 12 ft b. 14 ft c. 10 ft d. 18 ft

Explanation:

Step1: Use sine function

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 34^{\circ}$ and the hypotenuse is 25 ft, and the height $h$ is the opposite - side. So $\sin34^{\circ}=\frac{h}{25}$.

Step2: Solve for $h$

$h = 25\times\sin34^{\circ}$. Since $\sin34^{\circ}\approx0.5592$, then $h=25\times0.5592 = 13.98$ ft.

Step3: Round the result

Rounding 13.98 ft to the nearest foot gives 14 ft.

Answer:

b. 14 ft