Question

1. solve for z. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 60^{\circ}\), adjacent side \(= 8\), and hypotenuse \(=z\). So, \(\cos60^{\circ}=\frac{8}{z}\).

Step2: Substitute the value of \(\cos60^{\circ}\)

Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{8}{z}\).

Step3: Solve for \(z\)

Cross - multiply: \(z\times1 = 8\times2\).

Answer:

\(z = 16\)