BC = 18cm angle B = 45degree angle C = 75degree Find the side length AC.

The angles of a triangle add up to 180 °. So A = 180 ° <B – <C = 180 ° – 45 ° – 75 ° = 60 °.

According to the theorem of sines, the ratio of the side to the sine of the opposite angle is constant

for a given triangle:

BC / sin A = AC / sin B;

AC = BC * sin B: sin A;

sin 60 ° ≈ 0.866; sin 45 ° ≈ 0.707;

AC = 18 * 0.707: 0.866 ≈ 14.7 (cm).