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

Since one of the acute angles of a right-angled triangle is 450, then such a triangle is isosceles.

Let BC = AC = X cm.

Then, by the Pythagorean theorem, AB ^ 2 = BC ^ 2 + AC ^ 2 = 2 * X ^ 2.

2 * X ^ 2 = 9 * 2.

X ^ 2 = 9.

X = BC = AC = 3 cm.

Determine the area of the triangle.

Savs = AC * BC / 2 = 3 * 3/2 = 4.5 cm2.

Answer: The lengths of the legs are 3 cm, 3 cm, the area of the triangle is 4.5 cm2.