In a right-angled triangle ABC, angle C = 90, angle A = 30, AB = 10 Find AC, BC and angle B.

In a right-angled triangle, the leg, opposite an angle of 30 °, is equal to half the hypotenuse.
In our case, the leg BC = 1/2 AB = 5.
By the Pythagorean theorem, we find the second leg AC.
AC² = AB² – BC²
AC² = 100 – 25 = 75
AC = 5 √3
The angles of a triangle add up to 180 °.
By condition, two angles are known, therefore:
angle B = 180 ° – (90 ° + 30 °) = 180 ° – 120 ° = 60 °.
Or the sum of the acute angles in a right-angled triangle is 90 °, which means:
angle B = 90 ° – 30 ° = 60 °.
Answer: BC = 5, AC = 5 √3, angle B = 60 °.