In a right-angled triangle ABC, angle C is 90 degrees and angle A is 30 degrees.

In a right-angled triangle ABC, angle C is 90 degrees and angle A is 30 degrees. Find the legs of the triangle if the hypotenuse is 6cm.

In a right-angled triangle, the leg, opposite an angle of 30 °, is equal to half the hypotenuse.

Since the angle A is equal to 30 °, then:

СB = 1/2 AB = 1/2 * 6 = 3 (cm);

By the Pythagorean theorem:

AC² = AB² + BC²;

AB² = AC² – BC²;

AB² = 6² – 3² = 36 – 9 = 27 (cm²);

AB = √27 = √ (9 * 3) = 3 √3 (cm).