In a right-angled triangle, side AC = 3 cm, angle A = 45 °, find the hypotenuse AB.

Since the angle A is equal to 45, the other acute angle will also have a degree measure of 45 °. Since the sum of the acute angles of a right-angled triangle is 90, then:

90 ° – 45 ° = 45 ° – the value of another acute angle.

Since both acute angles have the same value, this right-angled triangle will also be isosceles, and the resulting angles will be the corners at the base. Accordingly, he has two equal legs:

AC = BC = 3 cm.

Using the Pythagorean theorem, we find the value of the hypotenuse AB:

AB = √ (3 ^ 2 + 3 ^ 2) = √ (9 + 9) = √ (18) = √ (9 * 2) = 3√ (2) cm – the length of the hypotenuse.

Answer: 3√ (2) see.