A 30-60-90 triangle is a special type of right triangle that has angles of 30 degrees, 60 degrees, and 90 degrees. It has the following properties:
The side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).
The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
To find the sides of a 30-60-90 triangle, you can use these properties.
If you know the length of the hypotenuse (the side opposite the 90-degree angle), you can find the length of the other two sides using the following formulas:
The side opposite the 30-degree angle: hypotenuse / 2
The side opposite the 60-degree angle: (√3) * (hypotenuse / 2)
If you know the length of one of the other two sides, you can use the above formulas to find the length of the hypotenuse and the other side.
For example, if you know the length of the side opposite the 30-degree angle, you can find the length of the hypotenuse by multiplying it by 2 and the length of the side opposite the 60-degree angle by multiplying it by √3
In summary:
The hypotenuse is always twice the length of the shorter leg.
The longer leg is √3 times the length of the shorter leg.
The hypotenuse is always the longest side in a 30-60-90 triangle.