To find the length of the shorter leg in a 30-60-90 triangle when the hypotenuse is 30, we can use the properties of this special triangle.
A 30-60-90 triangle has side lengths that are in a fixed ratio: the length of the shorter leg (opposite the 30-degree angle) is half the length of the hypotenuse, and the longer leg (opposite the 60-degree angle) is the length of the shorter leg multiplied by the square root of 3.
Given that:
- Hypotenuse = 30
- Shorter Leg = Hypotenuse / 2 = 30 / 2 = 15
So, the length of the shorter leg is 15. This calculated value falls in line with the properties of a 30-60-90 triangle, confirming it is accurate.