Question

find α in degrees.
α = ?°
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as $\sin\alpha=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the side opposite to angle $\alpha$ is $5$ and the hypotenuse is $13$. So, $\sin\alpha=\frac{5}{13}$.

Step2: Solve for $\alpha$

To find $\alpha$, we use the inverse sine function. $\alpha=\sin^{- 1}(\frac{5}{13})$.
Using a calculator, $\sin^{-1}(\frac{5}{13})\approx22.62^{\circ}$ (rounded to the nearest hundredth).

Answer:

$22.62$