In triangle ABC the angle at B is 90° and the angle at C is 30°. If AB = 9 cm, what is the length of BC?

In a 30°–60°–90° triangle the sides are in the ratio 1 : √3 : 2, with the shortest side opposite the 30° angle. Here AB is opposite the 30° angle at C, so AB is the short side and the hypotenuse AC = $2\times 9=18$ cm. Then BC = √$(18^2-9^2)=$ √243 = 9√3 cm (about 15.6 cm). Answering 18 cm gives the hypotenuse rather than the side asked for.