Question
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?Solution
According to the question, BC×AB = 1/2AC2 -----(1) BC2 + AB2 = AC2 -----(2) by Pythagoras Putting the value of AC2 in equation (2), BC2 + AB2 = 2BC × AB Or BC2 + AB2 - 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 900).
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