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).
4    9    28    99    ?   2105   12660
...900 Â Â Â 90Â Â Â 18Â Â Â ? Â Â Â Â 2.16Â Â Â Â 1.08
- What will come in place of the question mark (?) in the following series?
6, 24, 60, ?, 210, 336 Find the missing number in the given number series.
5, 9, 18, 34, 59, ?84, 97, ?, 162, 214, 279
- What will come in place of the question mark (?) in the following series?
712, ?, 576, 508, 440, 372 12, 27, ?, 113, 141, 285, 313
What will come in place of the question mark (?) in the following series?
16, ?, 480, 1920, 5760, 11520?, 32, 75, 144, 245, 384
What will come in place of the question mark (?) in the following series?
10, 410, ?, 710, 760, 785
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