Question

solve for x. round to the nearest hundredth if necessary.

x
19
29°

a. 10.53
b. 34.28
c. 39.19
d. 21.72

Explanation:

Step1: Use sine function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$, the opposite side to the angle is 19 and the hypotenuse is $x$. So, $\sin(29^{\circ})=\frac{19}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{19}{\sin(29^{\circ})}$. Since $\sin(29^{\circ})\approx0.4848$, then $x=\frac{19}{0.4848}\approx39.19$.

Answer:

c. 39.19