In triangle ABC, angle A is 60 degrees, angle C is 45 degrees, find the ratio BC / AB.

Given:

triangle ABC,

angle A = 60 degrees,

angle С = 45 degrees,

Find the ratio BC / AB -?

Decision:

Consider a triangle ABC, By the theorem of sines: the sides of a triangle are proportional to the sines of the opposite angles.

ВС / sin A = AB // sin С;

BC / AB = sin A / sin C;

BC / AB = sin 60 / sin 45;

BC / AB = √3 / 2: √2 / 2;

BC / AB = √3 / 2 * 2 / √2;

BC / AB = (√3 * 2) / (2 * √2);

BC / AB = (√3 * 1) / (1 * √2);

BC / AB = √3 / √2;

BC / AB = √6 / 2.

Answer: BC / AB = √6 / 2.