In a right-angled triangle, the hypotenuse is 70, and one of the acute angles is 45 °. Find the area of the triangle

SABC = AB * AC / 2
Let the angle equal to 45 ° be the angle B.
By the theorem on the sum of the angles of a triangle:
180 ° = ∠A + ∠B + ∠C
180 ° = 90 ° + 45 ° + ∠C
∠C = 45 °
Therefore, by the property of an isosceles triangle, triangle ABC is an isosceles triangle.
So AB = AC.
By the Pythagorean theorem:
BC2 = AB2 + AC2
BC2 = AB2 + AB2
70 ^ 2 = 2AB ^ 2
4900 = 2AB ^ 2
AB2 = 2450
SABC = AB * AC / 2
SABC = AB ^ 2/2 = 2450/2 = 1225
Answer: SABC = 1225

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