Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle TUV, we know the adjacent side to the 40° angle (TU = 64) and we want to find the hypotenuse (TV = x). We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(40^{\circ})=\frac{64}{x}$.

Step2: Solve for x

Cross - multiply to get $x\cos(40^{\circ}) = 64$. Then $x=\frac{64}{\cos(40^{\circ})}$.
We know that $\cos(40^{\circ})\approx0.766$. So, $x=\frac{64}{0.766}\approx83.6$.

Answer:

83.6