Question

solve for x. do not convert your answer to decimal form. rationalize the denomin and simplify your answer if necessary. draw 30° x 28

Explanation:

Step1: Use the cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the adjacent side is \(x\), and the hypotenuse is \(28\). So, \(\cos30^{\circ}=\frac{x}{28}\).

Step2: Substitute the value of \(\cos30^{\circ}\)

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\). Then \(\frac{\sqrt{3}}{2}=\frac{x}{28}\).

Step3: Solve for \(x\)

Cross - multiply: \(x = 28\times\frac{\sqrt{3}}{2}\). Simplify the expression: \(x = 14\sqrt{3}\).

Answer:

\(14\sqrt{3}\)