solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 2

Explanation:

Step1: Identify the trig - ratio

In right - triangle $\triangle UVT$, we know the adjacent side to the angle $70^{\circ}$ is $64$ and we want to find the hypotenuse $x$. We use the cosine function. The cosine of an angle $\theta$ in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(70^{\circ})=\frac{64}{x}$.

Step2: Solve for $x$

We can rewrite the equation $\cos(70^{\circ})=\frac{64}{x}$ as $x=\frac{64}{\cos(70^{\circ})}$. We know that $\cos(70^{\circ})\approx0.342$. Then $x = \frac{64}{0.342}\approx187.1$.

Answer:

$187.1$