Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $\triangle VUT$, we know the side adjacent to angle $T$ is $64$ and we want to find the hypotenuse $x$. We use the cosine function since $\cos(T)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(70^{\circ})=\frac{64}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{64}{\cos(70^{\circ})}$. Since $\cos(70^{\circ})\approx0.3420$, then $x = \frac{64}{0.3420}\approx187.1$.

Answer:

$187.1$