In a triangle ABC, Angle C is a straight line, AB = 10, the sine of angle B is 0.8. Find AC.

Explanation: The sine of the angle is equal to the ratio of the opposite leg to the hypotenuse. We find the opposite leg, then, through the Pythagorean theorem, we look for the adjacent leg.

sinA = CB / AB;

CB / 10 = 0.8;

CB = 8;

AB ^ 2 = AC ^ 2 + CB ^ 2;

AC = √ (AB ^ 2 – CB ^ 2);

AC = √ (10 ^ 2 – 8 ^ 2);

AC = √ (100 – 64);

AC = √36;

AC = 6.

Answer: 6.