In triangle ABC, angle C is 90, sin A = 4/5; AC = 12 find AB.

Given:
right-angled triangle ABC;
angle C = 90;
sin A = 4/5;
AC = 4;
Find: AB -?
Decision:
1) Let’s use the formula
cos ^ 2A + sin ^ 2A = 1;
cos ^ 2A = 1 – sin ^ 2A;
cos ^ 2A = 1 – 16/25;
cos ^ 2A = 25/25 – 16/25;
cos ^ 2A = 9/25;
cos A = 3/5;
2) Consider a right-angled triangle ABC. The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. Hence:
cos A = AC / AB;
AB = CA / cos A;
AB = 12: 3/5;
AB = 12 * 5/3;
AB = (12 * 5) / 3;
AB = (4 * 5) / 1;
AB = 20
Answer: AB = 20.