In a right-angled triangle, the hypotenuse is 5, the leg is 3. Find the other leg.

Let us denote the sides of the triangle given in the problem by a, b – legs, c – hypotenuse.

By condition, we are given a = 3 cm, c = 5 cm, we need to find b.

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs (according to the Pythagorean theorem):

a ^ 2 + b ^ 2 = c ^ 2;

b ^ 2 = c ^ 2 – a ^ 2;

Substitute numbers for a and b and solve the equation:

b ^ 2 = 5 ^ 2 – 3 ^ 2;

b ^ 2 = 25 – 9;

b ^ 2 = 16;

b = √16

b = 4 cm.

The second leg of the triangle is 4 cm.