In a right-angled triangle ABC (angle C = 90 degrees) AC = 5cm BC = 5√3 Find angle B and hypotenuse AB.

1. We calculate the value of the angle ABC, having previously calculated the tangent of this angle, equal to the ratio of the opposite leg of the AC to the adjacent leg of the BC:

The tangent of the angle ABC = AC / BC = 5 / 5√3 = 1 / √3.

Angle ABC = 30 °.

2. Using the Pythagorean theorem, we calculate the length of the side AB of the triangle, which is the hypotenuse of this triangle:

AB ^ 2 = AC ^ 2 + BC ^ 2.

AB = √AC ^ 2 + BC ^ 2 = √25 + 25 x 3 = √100 = 10 centimeters.

Answer: angle ABC = 30 °, AB = 10 centimeters.