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✓ Correct
B.((3-√3)/2)b
C.((3-√3)/4)b
D.((3+√3)/4)b
Explanation
Using QN = h and RN = h/√3, we have QR = QN - RN = h - h/√3 = h(√3-1)/√3 = b. So h = b√3/(√3-1) = b√3(√3+1)/2 = b(3+√3)/2. Therefore MN = (3+√3)b/2.
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