In an isosceles right-angled triangle, the hypotenuse is 3√2 cm. Find the sharp corners and legs.

1. Let us introduce the designation of the vertices of the triangle ABC. Angle ACB = 90 °. AB = AC. AB – hypotenuse.

2. To calculate the length of the legs AC and BC, we use the Pythagorean theorem:

AC ^ 2 + BC ^ 2 = AB ^ 2.

Since AB = AC according to the condition of the problem, this formula can be written in this form:

2 BC ^ 2 = AB ^ 2.

ВС = √АВ ^ 2/2.

ВС = √ (3√2) ^ 2 // 2 = √18 / 2 = √9 = 3 units.

3. Angle ABC = angle BAC = (180 ° – 90 °) / 2 = 90 °: 2 = 45 °.

Answer: the length of the legs AC and BC is equal to 3 units of measurement, acute angles BAC and ABC are equal to 45 °.