In a right-angled triangle ABC C = 90, B = 45, AB = 12cm. Find the remaining sides

In a triangle, the sum of the angles is 180 °.

Since we have a right-angled triangle, then:

sin A = cos B = 45 °.

Find the adjacent BC leg:

sin A = BC / AB;

BC = AB * sin A = 12 * sin 45 ° = 12 * 0.7 = 8.4 cm.

Find the side of the speaker:

cos B = AC / AB;

AC = AB * cos B = 12 * cos 45 ° = 12 * 0.7 = 8.4 cm.

Answer: AC = BC = 8.4 cm.