How to Solve a Right Triangle From Its Two Legs
Given the two legs of a right triangle, you can find everything else about it. This guide shows how, with the classic 3-4-5 example.
What is the Triangle Calculator?
Enter the two shorter sides of a right triangle, the legs that meet at the right angle. The tool uses Pythagoras to find the hypotenuse, halves the product of the legs for the area, adds all three sides for the perimeter, and uses inverse tangents to find both acute angles in degrees.
How to use it
- Enter the first leg, side a.
- Enter the second leg, side b.
- Calculate to see the hypotenuse, area, perimeter and angles.
Worked example
Legs 3 and 4 give hypotenuse 5, area 6, perimeter 12 and angles 53.13 and 36.87 degrees.
What is the hypotenuse of a right triangle with legs 3 and 4?
Square both legs and add them: 9 plus 16 is 25, and the square root of 25 is 5. So the hypotenuse is 5, the area is 6, the perimeter is 12, and the acute angles are about 53.13 and 36.87 degrees.
Frequently asked questions
Does this work for any triangle?
No. This tool is for right triangles only, where one angle is exactly 90 degrees and the two sides you enter meet at that angle.
Do the two angles add up to 90 degrees?
Yes. In a right triangle the two acute angles always add up to 90 degrees, since the third angle takes the other 90.