Question

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

Explanation:

Step1: Find the hypotenuse

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

Step2: Calculate \(\sin R\)

The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle R\), the opposite side to \(\angle R\) is \(ST = 5\) and the hypotenuse is \(RT=13\). So \(\sin R=\frac{5}{13}\approx0.38\).

Answer:

\(0.38\)