Understanding the Cotangent Function and Solving for cot 30° in a Right Triangle

cot 30°

To find the value of cot 30°, we first need to understand what the cotangent function represents

To find the value of cot 30°, we first need to understand what the cotangent function represents.

The cotangent function (cot) is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle. In other words, for a given angle in a right triangle, the cotangent of that angle is equal to the length of the adjacent side divided by the length of the opposite side.

In the case of cot 30°, we are dealing with an angle of 30 degrees. To evaluate cot 30°, we need to set up a right triangle where one of the angles is 30 degrees and determine the ratio of the adjacent side to the opposite side.

For a 30-60-90 right triangle, the sides are in a specific ratio. The side opposite the 30° angle is half the length of the hypotenuse, and the side adjacent to the 30° angle is equal to the length of the side opposite multiplied by √3.

Let’s denote the length of the side opposite the 30° angle as x. Then, the length of the adjacent side would be x√3, and the length of the hypotenuse would be 2x.

So in this case, the adjacent side is x√3, and the opposite side is x.

Therefore, cot 30° = x√3 / x = √3.

Therefore, the value of cot 30° is √3 or approximately 1.732.

More Answers: