In a right-angled triangle, the leg and hypotenuse are 7 and 25, respectively. Find the other leg of this triangle.

Given: right-angled triangle ABC;

angle C = 90;

leg AC = 7 centimeters;

hypotenuse AB = 25 centimeters.

Find: leg ВС -?

Solution:

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 = 25 ^ 2 – 7 ^ 2;

BC ^ 2 = 25 * 25 – 7 * 7;

BC ^ 2 = 625 – 49;

BC ^ 2 = 576;

BC = √ 576;

BC = 16 centimeters – length of the BC leg.

Answer: BC = 16 centimeters.