30-60-90 Triangles Page 3 of 5
Long Leg of a 30-60-90 Triangle
We've figured out the relationship between the short leg and hypotenuse of a 30-60-90 triangle, but what about the longer leg? How do we find that one? It's not quite as simple.
The Long Way: Use the Pythagorean Theorem
When you use the Pythagorean Theorem, it's important to label a, b, and c correctly. a and b are the legs that form the right angle (they make an L shape). c must be the hypotenuse (the side across from the right angle). In the triangle above, the 10 is the hypotenuse so we need to set c = 10.
We could leave the answer for the hypotenuse as the square root of 75 or round it and get a decimal answer. To show the shortcut relationship, we can simplify the square root of 75 instead. When you're simplifying a square root, look for factors of the number under the square root that are perfect squares. See if you can divide the number by 4, 9, 16, 25, etc. .