Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan R=\frac{PQ}{QR}\). Given \(QR = 97\), \(R = 33^{\circ}\), and \(PQ=x\). The formula for the tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan33^{\circ}=\frac{x}{97}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan33^{\circ}=\frac{x}{97}\) by \(97\). We get \(x = 97\times\tan33^{\circ}\). Using a calculator, \(\tan33^{\circ}\approx0.6494\). Then \(x=97\times0.6494\).

$$x = 97\times0.6494=63.0$$

Answer:

\(63.0\)