Question

find \\( \theta \\) in degrees.

\\( \theta = \\) \\( \square \\) \\( \square ^ { \circ } \\)

round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle $\theta$ is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the side opposite to $\theta$ is $7$ and the hypotenuse is $19$. So, $\sin\theta=\frac{7}{19}$.

Step2: Solve for $\theta$

To find $\theta$, we use the inverse sine function. $\theta=\sin^{- 1}(\frac{7}{19})$.
Using a calculator, $\sin^{-1}(\frac{7}{19})\approx21.69^{\circ}$ (rounded to the nearest hundredth).

Answer:

$21.69$