Question

find the value of \\( \sin r \\) rounded to the nearest hundredth, if necessary.
answer
\\( \sin r= \\)

Explanation:

Step1: Find the length of hypotenuse \(TR\)

By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 5\), \(b=12\), \(c = TR\)).
\(TR=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\)

Step2: Use the sine formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)

For \(\angle R\), the opposite side to \(\angle R\) is \(TS = 5\), and the hypotenuse \(TR=13\).
\(\sin R=\frac{TS}{TR}=\frac{5}{13}\approx0.38\)

Answer:

\(0.38\)