What is the value of tan 60°?

The value of tan 60° is derived from the properties of a 30-60-90 triangle. In such a triangle, the sides are in a specific ratio: the side opposite the 30° angle is half the length of the hypotenuse, while the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

To find the tangent of an angle, you calculate the ratio of the opposite side to the adjacent side. For tan 60°, the side opposite the angle (which corresponds to the height) is √3, and the adjacent side (the base) is 1. Therefore, the calculation for tan 60° is:

tan 60° = opposite/adjacent = √3/1 = √3.

Since √3 is approximately 1.732, the exact value of tan 60° is correctly represented as 1.732. This matches with the information provided in the answer option.