Question

find the length of side x to the nearest tenth.

Explanation:

Step1: Use the cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 60^{\circ}\), the adjacent side to the \(60^{\circ}\) angle is \(4\), and the hypotenuse is \(x\). So, \(\cos60^{\circ}=\frac{4}{x}\).

Step2: Solve for \(x\)

Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{4}{x}\). Cross - multiplying gives \(x = 4\times2\).

Answer:

\(x = 8.0\)