Answer:
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.
1. tan 90 degrees:
In a right triangle with a 90-degree angle, the opposite side of the angle is the longest side and the adjacent side is 0. Therefore, tan 90 = opposite/adjacent = undefined.
2. tan 45 degrees:
In a right triangle with a 45-degree angle, the opposite side and adjacent side are equal in length. Therefore, tan 45 = opposite/adjacent = 1.
3. tan 60 degrees:
In a right triangle with a 60-degree angle, the opposite side is √3 times the length of the adjacent side (based on the 30-60-90 triangle rule). Therefore, tan 60 = opposite/adjacent = √3.
4. tan 30 degrees:
In a right triangle with a 30-degree angle, the opposite side is half the length of the hypotenuse and the adjacent side is √3 times smaller than the hypotenuse (based on the 30-60-90 triangle rule). Therefore, tan 30 = opposite/adjacent = 1/√3 = √3/3.
Hope it helped :D
Explanation: