# In an isosceles right triangle, angle A is 45 degrees, AC-4, find AB

July 21, 2021 | education

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

Since we have a rectangular triangle and the angle C = 90 °, and by condition the angle A = 45 °, therefore, the angle B = 45 ° (180 – 90 – 45 = 45 °).

And from here it follows that our triangle is isosceles, and since the AC side = 4 cm, then the CB side = 4 cm.

To find the hypotenuse AB, one must use the Pythagorean theorem.

According to this theorem, the square of the hypotenuse is equal to the sum of the squares of two legs, that is:

AB² = AC² + CB² = 4² + 4² = 32

AB = √32 = 4√2