In triangle ABC, angle c is 90 degrees, angle a is 45 degrees, BC is 4. Find AB.

1) One angle in a right-angled triangle is 45 degrees.

The sum of two acute angles of a right-angled triangle is 90 degrees, then the second acute angle is also 90 degrees.

2) sin A = BC / AB;

∠ A = 45 °;

BC = 4;

Let us express AB from sin A = BC / AB;

AB * sin A = BC;

AB = BC / sin B = 4 / sin 45 = 4 / (√2 / 2) = 4/1 * 2 / √2 = 8 / √2 = 8 * √2 / (√2 * √2) = 8 * √2 / 2 = 4 * √2;

Answer: AB = 4 * √2.