The hypotenuse of a right-angled triangle is 13 cm, and the leg is 5 cm. What is the other leg?

Knowing the two sides of a right-angled triangle, the third side is found by the Pythagorean theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

c ^ 2 = a ^ 2 + b ^ 2.

c = 13 cm, a = 5 cm;

b ^ 2 = c ^ 2 – a ^ 2;

c ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144;

h = √144 = 12 (cm).

Answer. 12 cm.