Question

find α in degrees.
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle $\alpha$ is defined as $\sin\alpha=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the side opposite to $\alpha$ is $6$ and the hypotenuse is $10$. So, $\sin\alpha=\frac{6}{10}=0.6$.

Step2: Find the angle using the inverse sine function

We know that if $\sin\alpha = x$, then $\alpha=\sin^{- 1}(x)$. So, $\alpha=\sin^{-1}(0.6)$.
Using a calculator, $\sin^{-1}(0.6)\approx36.87^{\circ}$.

Answer:

$36.87$