Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle JIH\), we know the adjacent side (\(IH = 20\)) to the angle \(H=49^{\circ}\) and we need to find the hypotenuse (\(JH=x\)). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos H=\frac{IH}{JH}\).

Step2: Substitute the values

Substitute \(H = 49^{\circ}\) and \(IH = 20\) into the cosine formula. We get \(\cos49^{\circ}=\frac{20}{x}\).

Step3: Solve for \(x\)

Rearrange the formula to \(x=\frac{20}{\cos49^{\circ}}\).
We know that \(\cos49^{\circ}\approx0.6561\). Then \(x=\frac{20}{0.6561}\approx30.5\).

Answer:

\(x\approx30.5\)