In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?

Answer 1

sin A = 1/2
A = 30 degrees

sin is opposite over hypotenuse thus, BC/AC
BC = 8 (given)

thus 1/2 = 8/AC
AC = 16

cos A is cos 30degrees so cos A = (sqrt(3)) / 2

cos is always adjacent over hypotenuse thus, AB/AC
because AC = 16

sqrt3 /2 = AB/16

AB = 8 sqrt3