Question

find qr.

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( PQR \) with right angle at \( Q \), hypotenuse \( PR = 8 \), angle at \( P \) is \( 61^\circ \), and we need to find \( QR \) (opposite side to angle \( P \)). The sine function relates the opposite side and hypotenuse: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(61^\circ)=\frac{QR}{PR} \).

Step2: Substitute values and solve for \( QR \)

We know \( PR = 8 \) and \( \theta = 61^\circ \). Substitute into the formula: \( QR = PR \times \sin(61^\circ) \). Calculate \( \sin(61^\circ) \approx 0.8746 \), then \( QR = 8 \times 0.8746 \approx 6.9968 \). Rounding to the nearest tenth gives \( QR \approx 7.0 \).

Answer:

\( 7.0 \)