A 45°-45°-90° triangle is a special right triangle where the two legs are congruent and the hypotenuse is √2 times the length of the legs.
Let's say that the length of one leg is "x". Because the two legs are congruent, the length of the other leg is also "x".
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = a² + b²
c² = x² + x²
c² = 2x²
c = √(2x²) = x√2
Therefore, the length of the hypotenuse is x√2.
To find the missing sides of the triangle, we need to know one side length. If we are given the length of the hypotenuse or one of the legs, we can easily find the other sides.
For example, if we are given the length of one leg as 5 cm, we can find the lengths of the other sides as follows:
Legs = 5 cm
Hypotenuse = legs * √2 = 5 cm * √2 ≈ 7.071 cm
Therefore, the missing sides of the 45°-45°-90° triangle with one leg equal to 5 cm are approximately 5 cm and 7.071 cm.