Question

find each trigonometric ratio. give your answer as a fraction in simplest form.
answer attempt 1 out of 2
\\( \sin q= \\) \\( \sin r= \\)
\\( \cos q= \\) \\( \cos r= \\)
\\( \tan q= \\) \\( \tan r= \\)

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 16\), \(b=30\).

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Step2: Calculate \(\sin Q\)

\(\sin Q=\frac{\text{opposite}}{\text{hypotenuse}}\), opposite side to \(Q\) is \(30\), hypotenuse is \(34\).
\(\sin Q=\frac{30}{34}=\frac{15}{17}\)

Step3: Calculate \(\sin R\)

\(\sin R=\frac{\text{opposite}}{\text{hypotenuse}}\), opposite side to \(R\) is \(16\), hypotenuse is \(34\).
\(\sin R=\frac{16}{34}=\frac{8}{17}\)

Step4: Calculate \(\cos Q\)

\(\cos Q=\frac{\text{adjacent}}{\text{hypotenuse}}\), adjacent side to \(Q\) is \(16\), hypotenuse is \(34\).
\(\cos Q=\frac{16}{34}=\frac{8}{17}\)

Step5: Calculate \(\cos R\)

\(\cos R=\frac{\text{adjacent}}{\text{hypotenuse}}\), adjacent side to \(R\) is \(30\), hypotenuse is \(34\).
\(\cos R=\frac{30}{34}=\frac{15}{17}\)

Step6: Calculate \(\tan Q\)

\(\tan Q=\frac{\text{opposite}}{\text{adjacent}}\), opposite side to \(Q\) is \(30\), adjacent side to \(Q\) is \(16\).
\(\tan Q=\frac{30}{16}=\frac{15}{8}\)

Step7: Calculate \(\tan R\)

\(\tan R=\frac{\text{opposite}}{\text{adjacent}}\), opposite side to \(R\) is \(16\), adjacent side to \(R\) is \(30\).
\(\tan R=\frac{16}{30}=\frac{8}{15}\)

Answer:

\(\sin Q=\frac{15}{17}\), \(\sin R=\frac{8}{17}\), \(\cos Q=\frac{8}{17}\), \(\cos R=\frac{15}{17}\), \(\tan Q=\frac{15}{8}\), \(\tan R=\frac{8}{15}\)