Question

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

Step1: Identify the trigonometric ratio

We know the adjacent side ($a = 40$) and the hypotenuse ($c = 42$) of the right - triangle. We use the cosine function: $\cos\theta=\frac{a}{c}$.

Step2: Calculate the cosine value

$\cos\theta=\frac{40}{42}\approx0.9524$.

Step3: Find the angle

$\theta=\cos^{- 1}(0.9524)$. Using a calculator, $\theta\approx22^{\circ}$.

Answer:

$22^{\circ}$