In a right angled triangle the product of two sides is equal to half of the square of the third side...........

Quantitative Aptitude ( CCS) Geometry

In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be

60°

30°

45°

15°

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Explanation:

According to the question,
AB × BC = AC²/2
⇒ AC² = 2 × AB × BC
⇒ AB² + BC² = 2 × AB × BC
[By pythagoras theorem, AC² = AB² + BC²]
⇒ AB² + BC² – 2 × AB × BC = 0
⇒ (AB – BC)² = 0
⇒ AB = BC
∴ ∠C = ∠A
In ΔABC,
We know that the sum of the angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
⇒ ∠A + 90° + ∠A = 180°
[? ΔABC is an right-angled triangle]
⇒ 2∠A = 180° – 90° = 90°
⇒ ∠A = 45° and ∠C = 45° [? ∠A = ∠C]