In triangle ABC, angle C is 90 degrees sin A = 45, AC = 9, find AB.

Given: right-angled triangle ABC;

angle C = 90;

sin A = 4/5;

AC = 9;

Find: AB -?

Decision:

1) Let’s use the basic trigonometric 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 an angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse, and the leg is the AC side, and the hypotenuse is the AB side. Then we get:

cos A = AC / AB;

AB = CA / cos A;

AB = 9: 3/5;

AB = 9 * 5/3;

AB = (9 * 5) / 3;

AB = (3 * 5) / 1;

AB = 15

Answer: AB = 15.