Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric relation

Since it's a right - triangle and we know an angle and the adjacent side to find the hypotenuse, we use cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 67^{\circ}$, adjacent side to $\theta$ is 95 and hypotenuse is $x$. So $\cos(67^{\circ})=\frac{95}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{95}{\cos(67^{\circ})}$. We know that $\cos(67^{\circ})\approx0.3907$. Then $x=\frac{95}{0.3907}\approx243.1$.

Answer:

$243.1$