In a right-angled triangle, one of the legs is 6 cm, and the angle adjacent to it is 30 degrees.

In a right-angled triangle, one of the legs is 6 cm, and the angle adjacent to it is 30 degrees. Find the hypotenuse and the other leg of the triangle.

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

Let the length of the leg CB = x cm, then AB = 2x cm

By the Pythagorean theorem AB ^ 2 = AC ^ 2 + CB ^ 2.

4x ^ 2 = x ^ 2 + 36;

3x ^ 2 = 36;

x ^ 2 = 12;

x = 2√3 cm.

AB = 2 * 2√3 = 4√3 (cm)

Answer: the length of the leg is 2√3 cm, the length of the hypotenuse is 4√3 cm.