In triangle ABC, angle C is 90 °, leg BC = 6, height CD = 4.8. Find the length of the AC leg.

Consider a triangle ABC, <c = 90 °, AB – hypotenuse, AC and BC – legs. The height CD is perpendicular to AB, and divides the triangle into two rectangular ACD and CDB.
Consider a triangle CDB, <D = 90 ° CB – hypotenuse, DC and BD – legs.
We define sine <B as the ratio of the opposite leg to the hypotenuse:
sin B = CD / CB = 4.8 / 6 = 0.8
This sine corresponds to an angle <B = 54 °.
Now consider the triangle ABC, <c = 90 °, <B = 54 °.
We define the tangent of the angle <B, as the ratio of the opposite leg to the adjacent one:
tg B = AC / CB
Let us express AC from this expression:
AC = tg B * CB = tg 54 ° * 6 = 1.33 * 6 = 8
Answer: the AC leg is 8.