In a right-angled triangle ABC with right angle C leg AC = 8 cm, angle A is 45 degrees. Find hypotenuse AB.

If in a right-angled triangle one acute angle is 45 °, then the second acute angle will be 45 °. So a right-angled triangle is isosceles. The legs of an isosceles triangle are equal. CB = 8cm. We find the hypotenuse by the Pythagorean theorem: AB ^ 2 = AC ^ 2 + BC ^ 2.

AB ^ 2 = 8 ^ 2 + 8 ^ 2 = 64 + 64 = 128;

AB = √128 = 8√2 cm.

Answer: 8√2cm.