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 angles must be

Explanation

Let the sides of the triangle ABC(right angled at B) be 'a','b','c' and c is hypotenuse c2 Given that a × b = 2 ⇒ c2 =2ab We know that c2 = a 2 + b2 Substituting c2 value in above equation 2ab= a 2 + b2 ⇒ a 2 − 2ab + b2 = 0 ⇒ (a − b)2 = 0 ⇒a=b In a triangle, if two sides are equal then the opposite angles must be equal We know that ∠A + ∠B + ∠C = 180∘ Here ∠A= ∠C 90∘ + 2∠A=180∘ ∴ ∠A=∠C =45∘