In a right-angled triangle with an acute angle of 45 degrees, the hypotenuse is 3√2 cm

In a right-angled triangle with an acute angle of 45 degrees, the hypotenuse is 3√2 cm. Find the legs and the area of this triangle.

A right-angled triangle with an angle of 45 ° is isosceles, since the unknown angle is also 45 ° (180 ° – 90 ° – 45 °). Let us denote the length of each leg by the letter x and find them by the Pythagorean theorem:

x² + x² = (3√2) ²;

x² + x² = 11;

2x² = 11;

x² = 11/2;

x² = 5.5;

x = √5.5 – legs of the triangle;

Find the area of a right-angled triangle, which is equal to the half-product of the legs:

S = a * b / 2;

S = √5.5 * √5.5 / 2;

S = 5.5 / 2;

S = 2.75 cm².