In triangle ABC, angle C is 90 °, AB = 87, tgA = 7/3. find the height of the CH.

CH = AC * BC / AB
Let us denote the proportionality coefficient through x cm.
tgA = ВС / АС = 7 ÷ 3, then ВС = 7x cm, АС = 3x cm.
CH = 3x * 7x / 87 = 21 * x ^ 2/87
By the Pythagorean theorem, we find AB ^ 2 = BC ^ 2 + A ^ 2
AB ^ 2 = (3x) ^ 2 + (7x) ^ 2 = 9x ^ 2 + 49x ^ 2 = 58x ^ 2.
87 ^ 2 = 58x ^ 2
x ^ 2 = 87 ^ 2/58 = 87 * 3/2.
CH = (21 * 87 * 3) / (2 * 87) = 63/2 = 31.5 (cm).