Answer:
Dang, too difficult. Anyways,
In a right triangle, if one angle is 45 degrees, it means that the other two angles must be 45 degrees as well, making it an isosceles right triangle. Given that the length of one leg is 4√2 m, we can determine the lengths of the missing sides using the properties of an isosceles right triangle.
Since an isosceles right triangle has two equal legs, the lengths of the vertical leg and horizontal leg will be the same. Let's denote the length of each leg as "m."
Using the Pythagorean theorem, we can find the length of the hypotenuse (the side opposite the right angle) in terms of "m":
hypotenuse^2 = leg^2 + leg^2
hypotenuse^2 = m^2 + m^2
hypotenuse^2 = 2m^2
To find the length of the hypotenuse, we take the square root of both sides:
hypotenuse = √(2m^2) = √2 * m
Therefore, the length of the hypotenuse is √2 * m.
In summary, for the given isosceles right triangle with one leg measuring 4√2 m, both the vertical leg and horizontal leg will have a length of "m," while the length of the hypotenuse will be √2 * m.