Given a right triangle where angle $ACB$ is one of the non-right angles and the side opposite angle $ACB$ is $4$ units while the side adjacent to angle $ACB$ is $3$ units, which is the approximate measure of angle $ACB$?

• A. $31.0°$
• B. $53.1°$
• C. $36.9°$
• D. $59.0°$

Answer: (B)

Verified step by step guidance

1. Identify the given information: the side opposite to angle \( ACB \) is 4 units, and the side adjacent to angle \( ACB \) is 3 units in a right triangle.
2. Recall the trigonometric ratio for tangent, which relates the opposite side and the adjacent side of an angle in a right triangle: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).
3. Set up the equation using the given sides: \( \tan(ACB) = \frac{4}{3} \).
4. To find the measure of angle \( ACB \), take the inverse tangent (arctangent) of \( \frac{4}{3} \): \( ACB = \tan^{-1}\left(\frac{4}{3}\right) \).
5. Use a calculator to evaluate \( \tan^{-1}\left(\frac{4}{3}\right) \) to find the approximate angle measure in degrees.