Question

find qr.
write your answer as an integer or as a decimal rounded to the nearest tenth.
qr =

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(SQR\) with \(\angle Q = 90^{\circ}\), \(\tan R=\frac{QS}{QR}\). We know that \(\angle R = 41^{\circ}\) and \(QS = 6\). The formula for \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan R=\frac{QS}{QR}\), so \(QR=\frac{QS}{\tan R}\).

Step2: Substitute the values

Since \(QS = 6\) and \(R = 41^{\circ}\), and \(\tan41^{\circ}\approx0.8693\). Then \(QR=\frac{6}{\tan41^{\circ}}\).

$$QR=\frac{6}{0.8693}\approx6.9$$

Answer:

\(6.9\)