In triangle ABC, angle C is 90, AB = 12, sinA 3√11 / 10. Find AC

Given: right-angled triangle ABC;
angle C = 90;
sin A = 3√11 / 10;
AB = 12;
Find: AS -?
Solution:
1) Let’s use the formula
cos ^ 2A + sin ^ 2A = 1;
cos ^ 2A = 1 – sin ^ 2A;
cos ^ 2A = 1 – 9 * 11/100
cos ^ 2A = 100/100 – 99/100;
cos ^ 2A = 1/100;
cos A = 1/10;
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;
AC = AB * cos A;
AC = 12 * 1/10;
AC = 12/10;
AC = 1.2 centimeters.
Answer: 1.2 centimeters.