Question

trig #1
solve for x.
8.8
13.8
22.3
18.3

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 37^{\circ}\), adjacent side \(BC = 11\), and hypotenuse \(AB=x\). So, \(\cos(37^{\circ})=\frac{11}{x}\).

Step2: Solve for \(x\)

We know that \(\cos(37^{\circ})\approx0.8\). Then, from \(\cos(37^{\circ})=\frac{11}{x}\), we can rewrite it as \(x=\frac{11}{\cos(37^{\circ})}\). Substitute \(\cos(37^{\circ})\approx0.8\) into the formula: \(x=\frac{11}{0.8}=13.75\approx13.8\).

Answer:

13.8