Given a right triangle where side $LK$ is $7$ units, side $KJ$ is $24$ units, and $LJ$ is the hypotenuse, what is the measure of angle $LKJ$? Round to the nearest whole degree.

• A. $73°$
• B. $45°$
• C. $16°$
• D. $74°$

Answer: (A)

Verified step by step guidance

1. Identify the sides of the right triangle relative to the angle \( \angle LKJ \). Here, \( LK = 7 \) units, \( KJ = 24 \) units, and \( LJ \) is the hypotenuse.
2. Calculate the length of the hypotenuse \( LJ \) using the Pythagorean theorem: \( LJ = \sqrt{LK^2 + KJ^2} = \sqrt{7^2 + 24^2} \).
3. Determine which side is opposite and which is adjacent to the angle \( \angle LKJ \). Since the angle is at point \( K \), the side opposite is \( LK = 7 \) and the side adjacent is \( KJ = 24 \).
4. Use the tangent function to find the measure of the angle: \( \tan(\angle LKJ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{24} \).
5. Find the angle by taking the inverse tangent (arctangent) of \( \frac{7}{24} \): \( \angle LKJ = \tan^{-1}\left(\frac{7}{24}\right) \). Then round the result to the nearest whole degree.