Question

what is the value of x to the nearest hundredth? 14 65° x 15.45 33.13 12.69 30.02

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 65^{\circ}$, the opposite side to the angle $\theta$ is 14, and the hypotenuse is $x$. So, $\sin65^{\circ}=\frac{14}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{14}{\sin65^{\circ}}$. Since $\sin65^{\circ}\approx0.9063$, then $x=\frac{14}{0.9063}\approx15.45$.

Answer:

15.45