Question

1 multiple choice 12 points find sin(θ) for the following triangle. 12/13 5/12 5/13 12/5

Explanation:

Step1: Find the hypotenuse using Pythagorean theorem

In a right - triangle, \(a = 5\), \(b=12\). By \(c^{2}=a^{2}+b^{2}\), \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\).

Step2: Use the sine formula for a right - triangle

The formula for \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(\theta\), the opposite side to \(\theta\) is \(PR = 12\) and the hypotenuse \(QR=13\). So \(\sin\theta=\frac{12}{13}\).

Answer:

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