In a right triangle, if one angle is 90 degrees and one leg is 12 units while the hypotenuse is 13 units, what is the length of the other leg?

To find the length of the other leg in a right triangle when you know one leg and the hypotenuse, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides (the legs). This can be expressed mathematically as:

( a^2 + b^2 = c^2 )

where ( c ) is the length of the hypotenuse, and ( a ) and ( b ) are the lengths of the legs.

In this case, you have one leg measuring 12 units and the hypotenuse measuring 13 units. You can set up the equation as follows, letting ( b ) be the unknown length of the other leg:

( 12^2 + b^2 = 13^2 )

Calculating the squares:

( 144 + b^2 = 169 )

Next, you isolate ( b^2 ) by subtracting 144 from both sides:

( b^2 = 169 - 144 )

This simplifies to:

( b^2 =