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

May 31, 2020 | Education

| 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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