In triangle ABC, angle C is 90 degrees. AB = 20, tgA = 3/4. Find the sun.

In the ABC triangle it is known:
Angle C = 90 °;
AB = 20;
tg A = 3/4.
Let’s find the aircraft.
Decision:
1) cos ^ 2 a = 1 / (1 + tg ^ 2 a) = 1 / (1 + 9/16) = 1 / (16/16 + 9/16) = 1 / (25/16) = 16 / 25;
cos a = 4/5 = 0.8.
cos a = AC / AB;
From here we find AC = AB * cos a = 20 * 0.8 = 20 * 4/5 = 4 * 4 = 16;
3) Find the BC leg according to the Pythagorean theorem, since the hypotenuse and the second leg are known.
ВС = √ (20 ^ 2 – 16 ^ 2) = √ (400 – 256) = √144 = √12 ^ 2 = 12;
This means that the leg BC = 12.