Find the leg of a right-angled triangle if the hypotenuse is 5 cm and the larger leg is 4 cm.

Given: right-angled triangle ABC;

angle C = 90;

leg AC = 4 centimeters;

hypotenuse AB = 5 centimeters.

Find: the length of the BC leg -?

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 = 5 ^ 2 – 4 ^ 2;

BC ^ 2 = 5 * 5 – 4 * 4;

BC ^ 2 = 25 – 16;

BC ^ 2 = 9;

BC = √ 9;

BC = 3 centimeters – length of the BC leg.

Answer: BC = 3 centimeters.




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