Question

1 multiple choice 11 points find $\sin (\theta)$ for the following triangle. $\frac{12}{5}$ $\frac{12}{13}$ $\frac{5}{13}$ $\frac{5}{12}$

Explanation:

Step1: Find the hypotenuse

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

Step2: Use the sine formula

The formula for sine in a right - triangle is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to \(\theta\) is \(12\) and the hypotenuse is \(13\). So \(\sin(\theta)=\frac{12}{13}\)

Answer:

\(\frac{12}{13}\) (corresponding to the second option)