In a right-angled triangle ABC, angle C is straight, and leg BC = 2√5. Find the size of the second leg if angle ABC = 45.

Consider the triangle ABC. Because by condition, it is known that angle C is straight, that is, it is 90 °, and angle B is 45 °, then, knowing that in total all the angles of the triangle are 180 °, you can find out the degree measure of angle A:

180 – 90 – 45 = 45 (°).

Thus, we obtain that the triangle ABC has two equal angles at the base AB, which means that it is isosceles: the side of the AC is equal to the side of BC, i.e. the legs of the triangle are equal. Since BC = 2√5, then AC = 2√5.

Answer: the size of the second leg of the AC is 2√5.