In right triangle $ABC$, angle $C$ is the right angle, side $AB$ is $10$ units, and side $BC$ is $6$ units. What is the measure of angle $BAC$? Round to the nearest whole degree.

• A. $53$ degrees
• B. $60$ degrees
• C. $45$ degrees
• D. $37$ degrees

Answer: (D)

Verified step by step guidance

1. Identify the sides of the right triangle relative to the angle you want to find. Here, angle \( \angle BAC \) is the angle at vertex A. The side opposite to this angle is \( BC = 6 \) units, and the hypotenuse is \( AB = 10 \) units.
2. Recall the trigonometric ratio that relates the opposite side and the hypotenuse: the sine function. It is defined as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
3. Set up the equation using the sine function for angle \( \angle BAC \): \( \sin(\angle BAC) = \frac{BC}{AB} = \frac{6}{10} \).
4. To find the measure of \( \angle BAC \), take the inverse sine (arcsin) of \( \frac{6}{10} \): \( \angle BAC = \sin^{-1}\left(\frac{6}{10}\right) \).
5. Use a calculator to evaluate the inverse sine and then round the result to the nearest whole degree to get the measure of \( \angle BAC \).