Given a right triangle, what is the value of $tan(60°)$?

• A. $1$
• B. $\frac{1}{2}$
• C. $\sqrt{3}$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Recall that the tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Mathematically, this is expressed as \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).
2. Identify the angle given in the problem, which is \$60^\circ\(, and consider a right triangle where one of the angles is \)60^\circ$.
3. Use the properties of a 30-60-90 right triangle, where the sides are in the ratio \$1 : \sqrt{3} : 2\(, with the side opposite \)30^\circ\( being 1, opposite \)60^\circ\( being \)\sqrt{3}$, and the hypotenuse being 2.
4. Apply the tangent definition for the \$60^\circ\( angle: \)\tan(60^\circ) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{\sqrt{3}}{1}$.
5. Conclude that \(\tan(60^\circ) = \sqrt{3}\), which matches the known exact value for the tangent of \$60^\circ$.