Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 64^{\circ}\), adjacent side \(a = 7\), and hypotenuse \(x\). So, \(\cos64^{\circ}=\frac{7}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x=\frac{7}{\cos64^{\circ}}\). Since \(\cos64^{\circ}\approx0.4384\), then \(x=\frac{7}{0.4384}\approx16.0\).

Answer:

\(16.0\)