Question

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(VUT\) with \(\angle U = 90^{\circ}\), \(\angle T=70^{\circ}\), and \(UT = 64\). We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\cos T=\frac{UT}{VT}\).

Step2: Substitute the values

Since \(T = 70^{\circ}\), \(UT = 64\), and \(VT=x\), we have \(\cos70^{\circ}=\frac{64}{x}\).

Step3: Solve for \(x\)

$$x=\frac{64}{\cos70^{\circ}}$$

We know that \(\cos70^{\circ}\approx0.3420\).

$$x=\frac{64}{0.3420}\approx187.1$$

Answer:

\(x\approx187.1\)