Question

determine the length of de to the nearest tenth of a centimeter. select one: a. 13.9 cm b. 8.8 cm c. 3.7 cm d. 15.9 cm

Explanation:

Step1: Identify trigonometric relation

In right - triangle $DEF$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$, the opposite side to $\angle E$ is $DF = 7.7$ cm and the hypotenuse is $DE$. So, $\sin(29^{\circ})=\frac{DF}{DE}$.

Step2: Solve for $DE$

We can re - arrange the formula $\sin(29^{\circ})=\frac{7.7}{DE}$ to get $DE=\frac{7.7}{\sin(29^{\circ})}$. Since $\sin(29^{\circ})\approx0.4848$, then $DE=\frac{7.7}{0.4848}\approx15.9$ cm.

Answer:

d. 15.9 cm