tan60

tan60 refers to the trigonometric function tangent evaluated at an angle of 60 degrees. In the context of a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. For an angle of 60 degrees, this ratio has a specific, well-defined value.

The value of tan60 is an irrational number, commonly expressed as the square root of 3. This can be derived using a special 30-60-90 right triangle. In such a triangle, if the side opposite the 30-degree angle has a length of 1, then the side opposite the 60-degree angle has a length of the square root of 3, and the hypotenuse has a length of 2. Therefore, tan60 = (opposite side) / (adjacent side) = sqrt(3) / 1 = sqrt(3).

Numerically, the value of tan60 is approximately 1.7320508. This value is significant in various fields, including geometry, trigonometry, physics, and engineering, where calculations involving angles and ratios are frequently encountered. It is a fundamental constant that appears in many mathematical formulas and applications.