The leg of a right-angled triangle is 3 cm, and the hypotenuse is 5 cm. Calculate the length of the second leg.

Given: right-angled triangle ABC;

angle C = 90;

leg AC = 3 centimeters;

hypotenuse AB = 5 centimeters.

Find: leg ВС -?

Decision:

Consider a right-angled triangle ABC. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AC ^ 2 + BC ^ 2 = AB ^ 2 (we express the legs BC ^ 2 from this equality);

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 5 ^ 2 – 3 ^ 2;

BC ^ 2 = 5 * 5 – 3 * 3;

BC ^ 2 = 25 – 9;

BC ^ 2 = 16;

BC = √ 16;

BC = 4 centimeters – length of the BC leg.

Answer: BC = 4 centimeters.