# What is the value of tan(60°) in a given right triangle xyz?

Tan(60°) is a common trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In simpler terms, it is the ratio of the vertical height to the horizontal distance of a right triangle with a 60-degree angle.

Now, let’s assume we have a right triangle xyz where angle x measures 90 degrees, angle y measures 60 degrees, and angle z measures 30 degrees. The length of the sides opposite angles y and z are equal as the triangle is an equilateral triangle. If we label the length of these sides as “a,” then the length of the side opposite angle x would be 2a.

To find the value of tan(60°) in this right triangle, we would divide the length of the opposite side (a) by the length of the adjacent side (2a). Thus, the value of tan(60°) in this triangle would be 1/√3 or approximately 0.577.

In conclusion, the value of tan(60°) in a given right triangle xyz can be found by determining the ratio of the length of the opposite side to the length of the adjacent side. It is an important mathematical concept that has many applications in fields such as engineering, physics, and mathematics itself.