MATH CALCULATOR
Special Right Triangles Calculator
Efficiently calculate side lengths and angles of special right triangles.
What is the Special Right Triangles Calculator & How does it work?
Special right triangles are specific types of right-angled triangles with particular angle measures. The two most common types are the 45-45-90 triangle and the 30-60-90 triangle.
In a 45-45-90 triangle, the two legs are of equal length, and the hypotenuse is √2 times the length of each leg. The ratios of the sides are 1:1:√2.
In a 30-60-90 triangle, the sides are in the ratio 1:√3:2, where the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter leg.
In a 45-45-90 triangle, the two legs are of equal length, and the hypotenuse is √2 times the length of each leg. The ratios of the sides are 1:1:√2.
In a 30-60-90 triangle, the sides are in the ratio 1:√3:2, where the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter leg.
a = frac{c}{sqrt{2}} quad (45-45-90)
a = length of each leg, c = hypotenuse
Parameters
Result—
Frequently Asked Questions
What are the ratios for a 45-45-90 triangle?
In a 45-45-90 triangle, the two legs are equal, and the hypotenuse is √2 times the length of each leg. The ratio of the sides is 1:1:√2.
How do you find the side lengths of a 30-60-90 triangle?
In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. The side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter leg.
Can you explain the properties of a 45-45-90 triangle?
A 45-45-90 triangle has two equal legs and a hypotenuse that is √2 times the length of each leg. The side ratios are 1:1:√2.
What is the relationship between the sides in a 30-60-90 triangle?
In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times the length of the shorter leg.
How do I use this calculator for a 45-45-90 triangle?
Enter the length of one leg to find the lengths of the other leg and the hypotenuse. The hypotenuse will be √2 times the length of the entered leg.
What if I know the hypotenuse of a 30-60-90 triangle?
If you know the hypotenuse, divide it by 2 to get the shorter leg and multiply by √3 to find the longer leg.
Can this calculator handle both types of special right triangles?
Yes, this calculator can be used for both 45-45-90 and 30-60-90 triangles. Simply input the known side length to find the others.
Results are for informational purposes only and do not constitute professional advice.