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?
A. ( 3+ 3 2 )b
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
Related: Mathematics — Heights and Distances · All PYQ Banks