Calculating The Tangent Of 30°: A Step-By-Step Guide With Special Right Triangles

tan 30°

√3/ 3

The value of tan 30° is 0.577.

To determine this value, we need to use the trigonometric ratio of tangent. In a right angled triangle, tangent is defined as the ratio of opposite side to adjacent side.

To find the tangent of 30°, we can consider a 30°-60°-90° right angled triangle, where the angle opposite to the 30° is 60° and the hypotenuse is the longest side. It is a special triangle where the sides are in the ratio of 1:√3:2.

So, if we assume that the adjacent side is 1 unit, then the opposite side (which is opposite to 30°) will be √3 units and the hypotenuse will be 2 units.

Therefore, the value of tangent of 30° can be calculated as follows:

tan 30° = opposite side / adjacent side
= √3 / 1
= √3

However, we need to express this value as a decimal. To do so, we need to simplify the expression since √3 is not a terminating decimal.

We can do this by rationalizing the denominator. To rationalize the denominator, we multiply both numerator and denominator by the conjugate of the denominator:

tan 30° = √3 / 1 = (√3 / 1) x (√3 / √3) = 3 / √3

Now, we can simplify this expression by dividing both numerator and denominator by √3:

tan 30° = (3 / √3) x (√3 / √3) = 3√3 / 3 = √3

So, the value of tangent of 30° is √3, which is approximately equal to 0.577 when expressed as a decimal.

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