Find the legs of a right-angled triangle if its hypotenuse is 6 cm and one of the acute angles is 30 degrees.

Let a triangle ABC be given (angle A = 90 °).
By condition it is said that BC = 6 cm and angle B = 30 °.
According to the properties of a right-angled triangle: opposite an angle of 30 degrees lies a leg equal to half of the hypotenuse. So AC = BC / 2 = 6/2, AC = 3 cm.
By the Pythagorean theorem, we find the second leg – AB.
BC ^ 2 = AB ^ 2 + AC ^ 2
AB ^ 2 = BC ^ 2 – AC ^ 2
AB ^ 2 = 6 ^ 2 – 3 ^ 2
AB ^ 2 = 36 – 9
AB ^ 2 = 27
AB = 3√3
Answer: the first leg is 3 cm and the second leg is 3√3 cm.