In an acute-angled triangle ABC, the height AH is 6 √21 and the side of AB is 30 Find B.

The height, lowered from the apex of the triangle to the opposite side, forms a right angle with the opposite side, in which side HB, AH – legs, AB – hypotenuse.
Leg AH – leg opposite to the corner that we need to find. The ratio of the opposite leg to the hypotenuse is called the sinus.
Find angle B:
6√21 / 30 = √21 / 6.
Then the angle B = arcsin (√21 / 6).
This is not a tabular value, but using an engineering calculator, you can calculate that the angle B = 66.42 °.
ANSWER: 66.42 °.