Question

In ΔPQR, the measure of ∠R=90°, RQ = 12, QP = 37, and PR = 35. What is the value of the sine of ∠Q to the nearest hundredth?

Answer 1

To find the sine of angle \( Q \) in triangle \( \triangle PQR \), we can use the definition of the sine function, which is given by:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In triangle \( \triangle PQR \), where \( \angle R = 90^\circ \):
- The side opposite to \( \angle Q \) is \( PR \).
- The length of hypotenuse \( QP \) is \( 37 \).

The next step is to identify the lengths of the sides:
- \( PR = 35 \) (the side opposite to \( \angle Q \))
- \( QP = 37 \) (the hypotenuse)

Now we can compute \( \sin(Q) \):

\[
\sin(Q) = \frac{PR}{QP} = \frac{35}{37}
\]

Next, we perform the division:

\[
\frac{35}{37} \approx 0.9459459459
\]

Now, rounding to the nearest hundredth gives:

\[
\sin(Q) \approx 0.95
\]

Thus, the value of the sine of \( \angle Q \) to the nearest hundredth is:

\[
\boxed{0.95}
\]