In this calculator, the Greek symbols О± (alpha) and ОІ (beta) are used for the unknown angle measures. Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90В°) for side c, as shown below. The sides of a right triangle are commonly referred to with the variables a, b, and c, where c is the hypotenuse and a and b are the lengths of the shorter sides. In a right triangle, the side that is opposite of the 90В° angle is the longest side of the triangle, and is called the hypotenuse. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry. All that's left is finding the long leg.Related Triangle Calculator | Pythagorean Theorem Calculator Right triangleДЄ right triangle is a type of triangle that has one angle that measures 90В°. Since the value of x is the length of the short leg, we already have two out of three. If we know the length of the hypotenuse, we can figure out the rest. What are the sides of a 30-60-90 triangle that has a hypotenuse of 10? The long leg is opposite of the 60В° angle, and the short leg is opposite of the 30В° angle. Sometimes, knowing which side is the short leg and which is the long leg is confusing, but that's what angles are for. The hypotenuse is twice the length of the short leg. It's a really common mistake, but a quick look at our chopped-up Triforce will tell us why that's just not true. Notice that the long leg of the triangle is not twice the length of the short leg. That's the other reason we call it the Triforce triangle.

The thing is, now we have three formulas to remember: one for each side of the triangle. Subtract x 2 from both sides and then take the positive square root.

After all, we did cut it exactly in half. If we look at that hacked-up equilateral triangle, we can see that the hypotenuse of the right triangle equals twice the length of the shortest leg. We'll start as we did before, giving a shout out to Mr. Don't worry, it's nothing like trudging through Hyrule to rescue Princess Zelda. Magical, but just a smidgeon more work to do. Like the Gandalf triangle, knowing any side length of the Triforce triangle, which has angles of 30В°, 60В°, and 90В°, can tell us the other sides. Not one of those is a right triangle, but if we cut them in half, they will be. The other magical right triangle comes from an equilateral triangle, or what might be better known as the Triforce from The Legend of Zelda. As usual, we'll start with the formula we derived from the What is the length of this triangle's legs?ДЄnd like the magic poem says, we only need one side to figure out the Things are about to get magical.ДЇor every 45-45-90 triangle, one side can give us the lengths of all the sides. Taking the positive square root of both sides will tell us what the hypotenuse equals.ДЇactoring whatever's under the square root will simplify things. The magical thing about these triangles, though, is that a and b equal each other. If we throw the Pythagorean Theorem at them, we'll see why. More magical than Gandalf from The Lord of the Rings.

A little known fact about these triangles: they're Now we have two 45-45-90 isosceles triangles, with diagonal dДЄs our hypotenuse.

Special right triangles formulas