In a right-angled triangle, legs a and b are given hypotenuse c. Find its second leg if a = 5; c = 13

We write down the Pythagorean theorem, which says that the square of the leg is equal to the difference between the square of the hypotenuse and the second leg.

b ^ 2 = c ^ 2 – a ^ 2

Since we know the values of the hypotenuse and leg, we substitute them into the formula and get:

b ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

√144 = 12 cm.

Answer: The length of the second leg is 12 cm.