Question

find the value of sin r rounded to the nearest hundredth, if necessary.

(image of a right triangle rst with right angle at s, side st = 5, side sr = 12)

answer attempt 1 out of 2
sin r =
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Explanation:

Step1: Find the hypotenuse

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

Step2: Calculate \(\sin R\)

By the definition of sine in a right - triangle \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle R\), the opposite side to \(\angle R\) is \(ST = 5\) and the hypotenuse \(TR=13\).
\(\sin R=\frac{5}{13}\approx0.38\)

Answer:

\(0.38\)