In a right-angled triangle ABC, angle C is a straight line. find AB if AC √21, cosB = 0.4

Given: right-angled triangle ABC;
angle C = 90;
cos B = 0.4;
AC = 4;
Find: AB -?
Solution:
1) Let’s use the basic trigonometric formula
cos ^ 2B + sin ^ 2B = 1;
sin ^ 2B = 1 – sin ^ 2B;
sin ^ 2B = 1 – 0.16;
sin ^ 2B = 0.84;
sin B = √0.84.
2) Consider a right-angled triangle ABC. The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. Hence:
sin B = AC / AB;
AB = CA / sin B;
AB = √21: √0.84;
AB = (√21 * 10) / √84;
AB = 10/2;
AB = 5
Answer: AB = 5.