In a right-angled triangle ABC it is known that the angle is a = 30 degrees, and the leg AB = 4cm. find the hypotenuse.

In triangle ABC, angle B is straight, AC is hypotenuse. Angle A is opposite the leg BC, which is half the hypotenuse (by the property of the leg, opposite to the angle of 30 degrees). 1 way. We denote the leg BC = x, then AC = 2x. By the Pythagorean theorem: x ^ 2 + 16 = 4x ^ 2 => x ^ 2 = 16/3 => x = 4/3 multiply by the root of 3. AC = 2x = 8/3 multiply by the root of 3.2 … AB is adjacent to the angle A, which means that cos A = AB / AC <=> cos 30 = 4 / AC <=> 1/2 * √3 = 4 / AC => AC = 8/3 * √ 3.
Answer: The hypotenuse is 8/3 * √3.