Question

find the angle $\theta$ in the given right triangle. round answers to the
$\theta =$
question help: written example message instructor

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to \(\theta\) is \(9\) and the hypotenuse is \(13\). So, \(\sin\theta = \frac{9}{13}\).

Step2: Find the angle \(\theta\)

To find \(\theta\), use the inverse sine function \(\theta=\sin^{- 1}(\frac{9}{13})\). Using a calculator, \(\theta=\sin^{-1}(\frac{9}{13})\approx43.8^{\circ}\)

Answer:

\(43.8^{\circ}\)