Question

answer attempt 1 out of 8
\\(\sin r = \frac{16}{17}\\)
\\(\cos q = \frac{16}{17}\\)
\\(\sin r\\) and \\(\cos q\\) are equal because \\(\overline{pq}\\) is \\(\angle r\\) and \\(\angle q\\).
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Explanation:

Step1: Label right triangle parts

Let the right angle be $P$. So:

• For $\angle R$: opposite side $PQ=16$, hypotenuse $QR=17$
• For $\angle Q$: adjacent side $PQ=16$, hypotenuse $QR=17$

Step2: Calculate $\sin R$

$\sin R = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{16}{17}$

Step3: Calculate $\cos Q$

$\cos Q = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{16}{17}$

Step4: Relate sides to angles

Side $\overline{PQ}$ is opposite $\angle R$, adjacent to $\angle Q$. This makes $\sin R = \cos Q$ for complementary angles $\angle R$ and $\angle Q$.

Answer:

$\sin R = \frac{16}{17}$
$\cos Q = \frac{16}{17}$
$\sin R$ and $\cos Q$ are equal because $\overline{PQ}$ is opposite $\angle R$ and adjacent $\angle Q$.