Find the leg of a right-angled triangle if its hypotenuse is 13 cm and the other leg is 12 cm.

Knowing that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the legs, you can calculate the length of the leg knowing its hypotenuse and the size of the other leg.

Since c ^ 2 = a ^ 2 + b ^ 2, therefore, the unknown leg can be calculated by the formula:

a ^ 2 = c ^ 2 – b ^ 2

a = √c ^ 2 – b ^ 2 = √13 ^ 2 – 12 ^ 2 = √169 – 144 = √25 = 5 cm.

Answer: In a right-angled triangle with hypotenuse 13 and leg 12, the length of the second leg will be 5 cm.