# Find the hypotenuse of a right-angled triangle if one of the legs is 5 ^ 3 cm, and the angle adjacent to this leg is 30 degrees.

August 22, 2021 | education

| Given: right-angled triangle ABC;

angle C = 90;

leg AC = 5√3 centimeters = 125 centimeters;

angle A = 30 degrees.

Find: hypotenuse AB -?

Solution:

Consider a right-angled triangle ABC. In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then

BC = 1/2 * AB;

AB = 2 * BC

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;

AC ^ 2 + BC ^ 2 = 4BC ^ 2;

75 + BC ^ 2 = 4BC ^ 2;

3 * BC ^ 2 = 75;

BC ^ 2 = 25;

BC = √25;

BC = 5;

AB = 2 * 5 = 10 centimeters.

Answer: AB = 10 centimeters.

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