In a right-angled triangle, the square of the hypotenuse is twice the product…
2023
In a right-angled triangle, the square of the hypotenuse is twice the product of the other two sides. Then one of the acute angles of the triangle is
Answer: B. 45 degree — Key idea: use the Pythagorean relation and the given condition to relate the legs. Let the two legs of the right triangle be a and b, and the hypotenuse be c.…
- A.
30degree
- B.
45 degree
- C.
60 degree
- D.
15 degree
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Correct answer: B
Key idea: use the Pythagorean relation and the given condition to relate the legs.
Let the two legs of the right triangle be a and b, and the hypotenuse be c.
From the Pythagorean theorem: c^2 = a^2 + b^2.
The problem states: c^2 = 2ab.
Equate the two expressions for c^2: a^2 + b^2 = 2ab.
Rearrange: a^2 - 2ab + b^2 = 0, which is (a - b)^2 = 0.
Therefore a = b, so the triangle is isosceles with the two acute angles equal.
In an isosceles right triangle the acute angles are each 45°, so one acute angle is 45°.
Answer: 45°.