Question

find the measure of the missing angle to the nearest degree.
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Explanation:

Step1: Identify the trigonometric ratio

We use sine ratio since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, opposite side = 10 and hypotenuse = 39. So $\sin\theta=\frac{10}{39}$.

Step2: Calculate the angle

$\theta=\sin^{- 1}(\frac{10}{39})$. Using a calculator, $\theta=\sin^{-1}(0.25641)\approx15^{\circ}$.

Answer:

$15^{\circ}$