Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(HIJ\), we know the hypotenuse \(HJ = 94\) and we want to find the side \(x=HI\) opposite to the angle \(\angle J=72^{\circ}\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin(72^{\circ})=\frac{x}{94}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(72^{\circ})=\frac{x}{94}\) by \(94\).
We get \(x = 94\times\sin(72^{\circ})\).
Since \(\sin(72^{\circ})\approx0.9511\), then \(x=94\times0.9511 = 94\times\frac{9511}{10000}=\frac{94\times9511}{10000}=\frac{894034}{10000}=89.4034\approx89.4\).

Answer:

\(x = 89.4\)