Given a right triangle where one of the acute angles is $x$ and the lengths of the sides opposite and adjacent to $x$ are $3$ and $4$ respectively, what is the value of $x$ in degrees?

• A. $45$
• B. $36.87$
• C. $30$
• D. $53.13$

Answer: (B)

Verified step by step guidance

1. Identify the given information: the side opposite to angle \(x\) is 3, and the side adjacent to angle \(x\) is 4 in a right triangle.
2. Recall the definition of the tangent function in a right triangle: \(\tan(x) = \frac{\text{opposite}}{\text{adjacent}}\).
3. Set up the equation using the given side lengths: \(\tan(x) = \frac{3}{4}\).
4. To find the angle \(x\), take the inverse tangent (arctangent) of both sides: \(x = \tan^{-1}\left(\frac{3}{4}\right)\).
5. Use a calculator set to degree mode to evaluate \(x = \tan^{-1}\left(\frac{3}{4}\right)\) and find the measure of angle \(x\) in degrees.