Question

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

Explanation:

Step1: Use tangent function

In right - triangle \(PQR\), \(\tan R=\frac{PQ}{QR}\). Here, \(QR = 97\), \(R = 53^{\circ}\), and \(PQ=x\). The formula for the tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(53^{\circ})=\frac{x}{97}\).

Step2: Solve for \(x\)

We know that \(\tan(53^{\circ})\approx1.3270\). Then, \(x = 97\times\tan(53^{\circ})\). Substitute the value of \(\tan(53^{\circ})\) into the equation: \(x=97\times1.3270 = 128.719\).

Step3: Round to the nearest tenth

Rounding \(128.719\) to the nearest tenth gives \(x\approx128.7\).

Answer:

\(128.7\)