Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 49^{\circ}\), the adjacent side to \(\theta\) is \(IH = 20\), and the hypotenuse is \(JH=x\). So, \(\cos(49^{\circ})=\frac{20}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(x=\frac{20}{\cos(49^{\circ})}\).
We know that \(\cos(49^{\circ})\approx0.6561\). Then \(x=\frac{20}{0.6561}\approx30.5\).

Answer:

\(x\approx30.5\)