Find the leg of a right-angled triangle if the hypotenuse is 5 cm and the larger leg is 4 cm.
September 14, 2021 | education
| 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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