In a right-angled triangle ABC, the angle is from 90 degrees, the angle is 45 degrees

In a right-angled triangle ABC, the angle is from 90 degrees, the angle is 45 degrees, and the hypotinus is 10 cm. Find the legs ABC.

1. We calculate the degree measure of the angle ABC: 180 ° – 90 ° – 45 ° = 45 °.

2. The angles BAC and ABC at the side AB are equal. Therefore, triangle ABC is isosceles and its lateral sides BC and AC are equal.

3. Calculate the length of the legs using the Pythagorean theorem:

AC ^ 2 + BC ^ 2 = AB ^ 2.

We replace AC in this expression with BC, since they are equal:

BC ^ 2 + BC ^ 2 = AB ^ 2.

2BC ^ 2 = AB ^ 2.

BC ^ 2 = AB ^ 2/2.

BC ^ 2 = 100: 2 = 50.

BC = √50 = √25 x 2 = 5√2 centimeters.

Answer: the length of each of the legs of the ABC triangle is 5√2 centimeters.