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Consider the following for the two (02) items that follow: The top ( M ) of a tower is observed from three points P , Q and R lying in a horizontal straight line which passes directly along the foot ( N ) of the tower. The angles of elevations of M from P , Q and R are 30° , 45° and 60° respectively. Let PQ = a and QR = b . What is MN equal to?

Options

  1. A( 3+ 3 2 )b
  2. B( 3- 3 2 )b
  3. C( 3- 3 4 )b
  4. D( 3+ 3 4 )b

Correct answer

A. ( 3+ 3 2 )b

Step-by-step solution

Let MN = h be the height of the tower. The distances of points P , Q , and R from the foot of the tower N are given by: PN = h 30^ = h 3 QN = h 45^ = h RN = h 60^ = h 3 Given that P , Q , R lie on a straight line passing through N , the distance QR is: QR = QN - RN b = h - h 3 b = h ( 3 -1 3 ) h = b 3 3 -1 Rationalizing the denominator: h = b 3 ( 3 +1) ( 3 -1)( 3 +1) h = b(3+ 3 ) 3-1 h = ( 3+ 3 2 )b Answer: ( 3+ 3 2 )b

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