Question

find the measure of the missing angle. 20 13 41° 50° 49°

Explanation:

Step1: Identify adjacent/hypotenuse

We know the adjacent side ($13$) to the missing angle and the hypotenuse ($20$) of the right triangle, so we use the cosine function.

Step2: Calculate cosine value

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{13}{20} = 0.65$

Step3: Find inverse cosine

$\theta = \cos^{-1}(0.65)$
Calculate using a calculator: $\theta \approx 49.46^\circ$, which rounds to $49^\circ$.

Answer:

$49^\circ$