How to Solve for a Missing Right Triangle Length

The Pythagorean theorem states that a² + b² = c² in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.

In the left triangle, the measure of the hypotenuse is missing. Use the Pythagorean theorem to solve for the missing length.

1. Replace the variables in the theorem with the values of the known sides.

   48² + 14² = c²

2. Square the measures and add them together.

   

The length of the missing side, c, which is the hypotenuse, is 50.

The triangle on the right is missing the bottom length, but you do have the length of the hypotenuse. It doesn't matter whether you call the missing length a or b.

1. Replace the variables in the theorem with the values of the known sides.

   33² + b² = 183²

2. Square the measures, and subtract 1,089 from each side.

   

3. Find the square root of each side.

   

The length of the missing side is 180 units. That's not much shorter than the hypotenuse, but it still shows that the hypotenuse has the longest measure.