In triangle ABC AB = 10cm, angle B = 45 degrees, angle C = 60 degrees. Find the AC side.

In triangle ABC opposite angle C lies side AB, opposite angle B lies side AC. Angles B and C and side AB are known to us. ∠B = 45 °, ∠C = 60 °, AB = 10cm. To find the unknown side of AC, we apply the theorem of sines: The sides of a triangle are proportional to the sines of the opposite angles. a / sin α = b / sin β = c / sin γ.

AC / sin B = AB / sin C;

AC * sin C = AB * sin B;

AC = (AB * sin B) / sin C;

AC = (10 * sin 45 °) / (sin 60 °) = (10 * (√2) / 2) / ((√3) / 2) = 5√2 * 2 / √3 = 10√ (2 / 3) (cm).

Answer. 10√ (2/3) cm.