Question

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

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 65^{\circ}$, the adjacent side to the angle $\theta$ is 14, and the hypotenuse is $x$. So, $\cos65^{\circ}=\frac{14}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{14}{\cos65^{\circ}}$. Since $\cos65^{\circ}\approx0.4226$, then $x=\frac{14}{0.4226}\approx33.13$.

Answer:

33.13