In triangle ABC, angle A = 90 ‘, angle B = 30’, AB = 6cm. Find the sides of the triangle.

Let’s build a triangle ABC.
Angle A is 90 degrees by convention.
Angle B is 30 degrees by convention.
Therefore, the angle C = 180 – 90 -30 = 60 degrees.
From the theorem on legs, we know that a leg of a right-angled triangle located at an opposite angle of 30 degrees is equal to half of the hypotenuse.
So BC = 2 AC = 2 * 6 = 12 cm.
Next, using the Pythagorean theorem, we find the unknown side.
It is known from the theorem that: ВС = √ ((BA ^ 2) + (AC ^ 2)).
Hence AB = √ ((BC ^ 2) – (AC ^ 2)) = √ ((12 ^ 2) – (6 ^ 2)) = √ (144-36) = √ 108 = 6 * √ 3.
Answer: AC = 6; BC = 12; AB = 6 √ 3.