A right-angled triangle ABC is given an angle with a straight line. Find the length of the leg

A right-angled triangle ABC is given an angle with a straight line. Find the length of the leg of this triangle if AB = 5 √2 and the angle ABC = 45

In triangle ABC angle C = 90º, angle B = 45º. Find angle A:

Angle A = 180º – 90º – 45º = 180º – 135º = 45º.

That is, angle A = angle B = 45º. Hence, triangle ABC is isosceles, where AC = BC. In addition, this triangle is also rectangular. Hence, the Pythagorean theorem can be applied to it. According to her:

AB² = AC² + BC².

Since the triangle is isosceles, this formula can be written as follows:

AB² = 2AC².

From here

AC = √ (AB² / 2) = AB√1 / 2 = (√2 / 2) * AB.

Find the leg length AC:

AC = (√2 / 2) * 5√2 = (5 * 2) / 2 = 5.

Answer: the legs of triangle ABC are equal to AC = BC = 5.