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.
More Answers:
[next_post_link]