In a right triangle, one leg has length $5$ and the other leg has length $12$. What is the approximate degree measure of the angle opposite the leg of length $5$?

• A. $12.0°$
• B. $65.0°$
• C. $22.6°$
• D. $41.4°$

Answer: (C)

Verified step by step guidance

1. Identify the sides of the right triangle: the two legs are 5 and 12, and the right angle is between them.
2. Recall that the angle opposite the leg of length 5 can be found using the sine function, since sine relates the opposite side to the hypotenuse: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).
3. First, find the length of the hypotenuse using the Pythagorean theorem: \(\text{hypotenuse} = \sqrt{5^2 + 12^2}\).
4. Calculate \(\sin(\theta)\) by dividing the length of the opposite side (5) by the hypotenuse found in the previous step: \(\sin(\theta) = \frac{5}{\text{hypotenuse}}\).
5. Finally, find the angle \(\theta\) by taking the inverse sine (arcsin) of the value: \(\theta = \arcsin\left(\frac{5}{\text{hypotenuse}}\right)\), which will give the angle in degrees.