How to Work with 306090Degree Triangles
All 306090degree triangles have sides with the same basic ratio. If you look at the 30–60–90degree triangle in radians, it translates to the following:
In any 306090 triangle, you see the following:

The shortest leg is across from the 30degree angle.

The length of the hypotenuse is always two times the length of the shortest leg.

You can find the long leg by multiplying the short leg by the square root of 3.
Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60degree angle.
The figure illustrates the ratio of the sides for the 306090degree triangle.
If you know one side of a 306090 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:

Type 1: You know the short leg (the side across from the 30degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.

Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

Type 3: You know the long leg (the side across from the 60degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.
Finding the other sides of a 306090 triangle when you know the hypotenuse.
In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?
Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side: