# In a right-angled triangle, the hypotenuse is 82 and one of the acute angles is 45∘. Find the area of the triangle.

October 14, 2021 | education

| Let ABC be a given triangle.

∠С = 180 ° – 90 ° – 45 ° = 45 °.

Because the triangle is isosceles, then AB = AC.

By the Pythagorean theorem BC ^ 2 = AC ^ 2 + BC ^ 2.

Let AB = AC = x, then x ^ 2 + x2 = 82 ^ 2;

2x ^ 2 = 6724;

x ^ 2 = 3362.

S = ½ AC * AB = ½ * x ^ 2 = ½ * 3362 = 1681.

Answer: the area of the triangle is 1681.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.