In a right-angled triangle, the angle C is 45 degrees, and the AB side is 4 cm. How to find the AC side.

Option number 1 (angle A is the right angle).

Then the sides AB and AC will be the legs of the triangle.

Let us determine what the angle B will equal if from the condition we know that the angle C is equal to 45 °:

90 – 45 = 45.

That is, the triangle is isosceles, then AB = AC.

Answer: AC = 4 cm.

Option number 2 (angle B is a right angle)

Then the AC side will be the hypotenuse.

Let us determine what the length of the AC side will be when we know that the length of the AB leg is 4 cm:

sin C = AB / AC;

AC = 4: 1 / √2 = 4√2.

Answer: AC = 4√2 cm.