Right Triangle Calculator

A right triangle is any triangle that contains one 90-degree angle. The side opposite that right angle is the hypotenuse, which is always the longest side. The other two sides are called legs, often labeled a and b, with the hypotenuse labeled c.

The Pythagorean theorem states that for any right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2. If you know any two sides, you can find the third. For legs 3 and 4, the hypotenuse is sqrt(3^2 + 4^2) = sqrt(25) = 5.

SOH-CAH-TOA is a memory aid for the three basic trig ratios in a right triangle: Sin = Opposite / Hypotenuse, Cos = Adjacent / Hypotenuse, Tan = Opposite / Adjacent. "Opposite" and "adjacent" are always relative to the angle you are working with, not the right angle.

A 30-60-90 triangle has angles of 30, 60, and 90 degrees. Its sides are always in the ratio 1 : sqrt(3) : 2, where the shortest leg is opposite the 30-degree angle and the hypotenuse is twice that shortest leg. For example, legs of 1 and sqrt(3) give a hypotenuse of 2.

A 45-45-90 triangle is an isosceles right triangle: both legs are equal and the two acute angles are each 45 degrees. The sides follow the ratio 1 : 1 : sqrt(2), so a hypotenuse is always the leg length multiplied by sqrt(2). For legs of 5, the hypotenuse is 5 x sqrt(2), or about 7.071.