find the sine of $angle r$.\nsimplify your answer and write it as a proper fraction, improper fraction, or…

Explanation:

Step1: Recall sine definition for right triangles

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle R$

Opposite side to $\angle R$ is $QP = 72$. First calculate hypotenuse $RP$ using Pythagorean theorem: $$RP = \sqrt{RQ^2 + QP^2} = \sqrt{65^2 + 72^2}$$ $$RP = \sqrt{4225 + 5184} = \sqrt{9409} = 97$$

Step3: Compute $\sin(R)$

Substitute values into sine formula: $$\sin(R) = \frac{72}{97}$$

Answer:

$\frac{72}{97}$