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.
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