Question

solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 3 x = submit answer

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 72^{\circ}\), the opposite side is \(x\), and the hypotenuse is \(94\). 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 \(x=94\times0.9511 = 94\times\frac{\sin(72^{\circ})}{1}\).
\(x\approx94\times0.9511=94\times\frac{9511}{10000}\approx94\times0.9511 = 89.4\)

Answer:

\(x = 89.4\)