Question

find the sine of ∠k.
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
sin(k) =

Explanation:

Step1: Recall Sine Definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle K$, the opposite side to $\angle K$ is $IJ = 72$, and we need to find the hypotenuse $KJ$.

Step2: Calculate Hypotenuse

Using the Pythagorean theorem: $KJ^2 = KI^2 + IJ^2$. Substitute $KI = 65$ and $IJ = 72$:
$KJ^2 = 65^2 + 72^2 = 4225 + 5184 = 9409$. Then $KJ = \sqrt{9409} = 97$.

Step3: Compute $\sin(K)$

$\sin(K) = \frac{\text{opposite to } K}{\text{hypotenuse}} = \frac{IJ}{KJ} = \frac{72}{97}$.

Answer:

$\frac{72}{97}$