Question

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

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 75^{\circ}\), adjacent side \(PQ = 8\), and hypotenuse \(OQ=x\). So, \(\cos75^{\circ}=\frac{8}{x}\).

Step2: Solve for \(x\)

We know that \(\cos75^{\circ}\approx0.2588\). Then \(x=\frac{8}{\cos75^{\circ}}\). Substitute the value of \(\cos75^{\circ}\): \(x=\frac{8}{0.2588}\approx31.0\).

Answer:

\(x\approx31.0\)