In a right-angled triangle ABC, two angles are set at 30 and 60 degrees. Corner C straight AC = 8cm. Find AB.

There are two options for this problem. But first, let’s remember what the sine (sin) of an angle is: sine is the ratio of the opposite leg to the hypotenuse. Based on this, the sine of angle B will be equal to:

sin B = AC: AB.

If the angle B is 30o, then sin B will be 1/2. Then the length AB will be:

AB = AC: sin B = 8: 1/2 = 16 (cm).

However, it is also possible that the angle B is 60 °. Then sin B will be equal to √3 / 2, and the length AB will be:

AB = AC: sin B = 8: √3 / 2 = 16 / √3 (cm).

Answer: i.e., AB = 16 cm or 16 / √3 cm.