How to Find the Tangent of 30 Degrees | Trigonometric Calculation Using a 30-60-90 Triangle

tan 30°

The tangent of 30 degrees can be found by using the trigonometric function tan(x)

The tangent of 30 degrees can be found by using the trigonometric function tan(x). In this case, x is equal to 30 degrees.

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In the context of a 30 degree angle, we can set up a right triangle where the angle opposite the side we are interested in is 30 degrees.

Using the special right triangle known as the 30-60-90 triangle, we know that in a triangle where the angles are 30, 60, and 90 degrees, the side opposite the 30 degree angle is half the length of the hypotenuse, and the side adjacent to the 30 degree angle is the height of the triangle.

Therefore, in this case, the opposite side has a length of 1 and the adjacent side has a length of √3. The tangent of 30 degrees is then given by:

tan(30°) = opposite/adjacent = 1/√3 = (√3)/3.

So, the value of tan(30°) is (√3)/3 or approximately 0.577.

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