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 \(HI=x\) which is opposite to the angle \(J = 72^{\circ}\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin J=\frac{HI}{HJ}\).

Step2: Substitute the values

Substitute \(J = 72^{\circ}\), \(HI=x\), and \(HJ = 94\) into the sine formula. We get \(\sin(72^{\circ})=\frac{x}{94}\).

Step3: Solve for \(x\)

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

Answer:

\(x\approx89.4\)