In a right triangle, if the length of the adjacent side is $1$ and the length of the opposite side is $\sqrt{3}$, what is the measure of the angle (in degrees) opposite the side of length $\sqrt{3}$?

• A. $30°$
• B. $60°$
• C. $90°$
• D. $45°$

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle relative to the angle we want to find. The side opposite the angle is given as \(\sqrt{3}\), and the adjacent side is 1.
2. Recall the definition of the tangent function in a right triangle: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).
3. Set up the equation using the given side lengths: \(\tan(\theta) = \frac{\sqrt{3}}{1} = \sqrt{3}\).
4. To find the angle \(\theta\), take the inverse tangent (arctangent) of \(\sqrt{3}\): \(\theta = \tan^{-1}(\sqrt{3})\).
5. Use your knowledge of special angles or a calculator to determine that \(\tan^{-1}(\sqrt{3})\) corresponds to \$60^\circ$.