In triangle ABC, side BC = 35cm, angle B is 40 °, angle C is 120 °. Find the angle A and sides AB, AC.

Find the angle A of the triangle, knowing the other two angles:
A = 180 – (40 + 120) = 20º.

To find the unknown sides of a triangle, we use the sine theorem:
ВС / sin A = AB / sin C = AC / sin B;

AB = BC * sin 120º / sin 20º = 35 * 0.866 / 0.342 = 88.626 cm.

AC = BC * sin 40º / sin 20º = 35 * 0.643 / 0.342 = 65.804 cm.

Answer: the triangle has sides AB = 88.626 cm; AC = 65.804 cm; angle A is 20 degrees.