Question

find the length of the side labeled x

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 58^{\circ}\), the hypotenuse is \(21\), and the side opposite to the \(58^{\circ}\) angle is \(x\). So, \(\sin(58^{\circ})=\frac{x}{21}\).

Step2: Solve for \(x\)

We know that \(\sin(58^{\circ})\approx0.848\). Then \(x = 21\times\sin(58^{\circ})\). Substitute \(\sin(58^{\circ})\approx0.848\) into the equation: \(x\approx21\times0.848 = 17.808\approx17.4\) (assuming some rounding differences in the problem - set values).

Answer:

\(17.4\)