In a right angle triangle, the product of two sides is half of the square of the third side (i.e., hypotenuse). Accordingly find out the acute angle?

According to the question, BC×AB = 1/2AC^{2} -----(1) BC^{2} + AB^{2} = AC^{2} -----(2) by Pythagoras Putting the value of AC^{2} in equation (2), BC^{2} + AB^{2 } = 2BC × AB Or BC^{2} + AB^{2} - 2BC × AB = 0 Or (BC – AB)^{2} = 0 Or BC – AB = 0 Or BC = AB Hence ∠BAC = ∠BCA = 45 (As sum of two angles other right angle in a right angle triangle is 90^{0}).

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