Understanding Tangent 60 Degrees | Calculation and Decimal Approximation

tan 60

The tangent of 60 degrees (tan 60) is equal to the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle

The tangent of 60 degrees (tan 60) is equal to the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In other words, it is the slope of the line passing through the origin and a point on the unit circle at an angle of 60 degrees.

To find the value of tan 60, we can use the unit circle or trigonometric identities. The unit circle is a circle with a radius of 1 unit, and the angle measured counter-clockwise from the positive x-axis determines a point on the unit circle.

For the angle 60 degrees, it is located in the first quadrant on the unit circle. The coordinates of the corresponding point on the unit circle are (√3/2, 1/2), where the x-coordinate (√3/2) represents the adjacent side and the y-coordinate (1/2) represents the opposite side.

Using this information, we can calculate tan 60 by dividing the opposite side by the adjacent side:
tan 60 = (opposite side) / (adjacent side) = (1/2) / (√3/2) = 1 / √3 = √3 / 3.

Therefore, the exact value of tan 60 is √3 / 3, which is an irrational number. In decimal approximation, tan 60 is approximately 1.73205.

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