Question

1. the hypotenuse of the right triangle δpqr shown below is 16 feet long. the sine of ∠p is $\frac{3}{5}$. about how many feet long is $overline{qr}$? f. 8.0 g. 9.6 h. 12.4 j. 14.3 k. 15.4

Explanation:

Step1: Recall sine - definition

In right - triangle $\triangle PQR$, $\sin(P)=\frac{QR}{PR}$.

Step2: Substitute given values

We know that $\sin(P)=\frac{3}{5}$ and $PR = 16$. So, $\frac{QR}{16}=\frac{3}{5}$.

Step3: Solve for $QR$

Cross - multiply: $QR=\frac{3\times16}{5}=\frac{48}{5}=9.6$.

Answer:

G. 9.6