Question

value: 2
solve for x. round to the nearest hundredth if necessary.
29°
19
x

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

Explanation:

Step1: Identify trigonometric relation

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, $\sin29^{\circ}=\frac{19}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{19}{\sin29^{\circ}}$. Since $\sin29^{\circ}\approx0.4848$, then $x = \frac{19}{0.4848}\approx39.19$.

Answer:

C. 39.19