In a right-angled triangle ABC, angle C is 90 degrees, side AC is 5 cm, side CB is 5√3, find angle B, hypotenuse AB and angle A

By the Pythagorean theorem, in a right-angled triangle ABC, we determine the length of the hypotenuse AB. AB ^ 2 = AC ^ 2 + BC ^ 2 = 25 + 75 = 10.

AB = 10 cm.

Since the AB leg is two times shorter than the AB hypotenuse, AB / AC = 10/5 = 2, the angle opposite the AC leg is 30.

Angle ABC = 30, then angle BAC = (90 – ABC) = (90 – 30) = 60.

Answer: The length of the hypotenuse AB is 10 cm, angle B is 300, angle A is 60.