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

According to the condition of the problem, the lengths of the legs AC and BC of the right-angled triangle ABC are 5 cm and 5√3 cm, respectively.

We find the length of the hypotenuse AB of a given triangle using the Pythagorean theorem:

| AB | = √ (5 ^ 2 + (5√3) ^ 2) = √ (25 + 25 * 3) = √ (25 + 75) = √100 = 10 cm.

We find the value of the angle B using the theorem of sines:

| AC | / sin (B) = | AB | / sin (90 °);

5 / sin (B) = 10;

sin (B) = 5/10;

sin (B) = 1/2.

Since the angles at the hypotenuse in a right triangle are acute, the value of the angle B is 30 °.

Answer: | AB | = 10 cm, ∠В = 30 °.