How to Calculate the Tangent of 30 Degrees (tan 30) | Trigonometric Function Explained

tan30

The term “tan” stands for tangent, which is a trigonometric function used to calculate the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle

The term “tan” stands for tangent, which is a trigonometric function used to calculate the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle.

In this case, the given value “tan30” refers to finding the tangent of the angle 30 degrees.

To find the tangent of 30 degrees, we can use the definition of the tangent function:

tan(theta) = opposite/adjacent

In a right triangle, one angle is always 90 degrees and the sum of the angles is 180 degrees. If we have an angle of 30 degrees, the other acute angle will be 60 degrees.

To calculate the tangent of 30 degrees, we need to consider a right triangle where the angle opposite to 30 degrees is labeled as “A” and the side adjacent to it is labeled as “B.” The side opposite to the 90-degree angle is labeled as “C.”

Using this right triangle, let’s calculate the values of the opposite and adjacent sides:

A = opposite side
B = adjacent side
C = hypotenuse

In a 30-60-90 degrees right triangle, the side opposite to the 30 degrees angle is A, the side opposite to the 60 degrees angle is B, and the side opposite to the 90 degrees angle is C.

In this case, the side opposite to the 30 degrees angle is labeled as A (which is the height of the triangle), and the side adjacent to the 30 degrees angle is labeled as B (which is the base of the triangle). The hypotenuse is labeled as C.

By convention, in a 30-60-90 degrees triangle, the ratios between the sides are as follows:

A : B : C = 1 : √3 : 2

Now, as we need to calculate the tangent of 30 degrees, we can use the formula:

tan(30 degrees) = opposite/adjacent = A/B

From the ratio mentioned above, we know that A = 1 and B = √3. Substituting these values into the formula, we have:

tan(30 degrees) = 1/√3

To rationalize the denominator, we multiply both the numerator and denominator by √3:

tan(30 degrees) = (1 * √3) / (√3 * √3) = √3 / 3

Therefore, the value of tan(30 degrees) is √3 / 3.

In decimal form, this value is approximately 0.577.

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