In a triangle, the two angles are 45 and 90 degrees, and the larger side is 20 cm. Find the other sides of the triangle.

Because the sum of the interior angles of the triangle is 180 °, then we find the third unknown angle:
180 ° – 90 ° – 45 ° = 45 °.
A triangle with one of the 90 ° angles is rectangular and its large side is the hypotenuse.
Let the length of the legs be x cm, then by the Pythagorean theorem x ^ 2 + x ^ 2 = 20 ^ 2.
Let’s solve the equation.
2x ^ 2 = 400;
x ^ 2 = 200;
| x | = 10√2.
We take only the positive root of the equation, since the side cannot be negative.
x = 10√2 (cm).
Answer: the other sides of the triangle are 10√2 cm.