A man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be 45°. The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?
A.tan⁻¹(1/2)
B.tan⁻¹(1/3)✓ Correct
C.tan⁻¹(2/3)
D.tan⁻¹(3/4)
Explanation
PM = 100, PR = 50 (chimney height). Q is the highest point of smoke directly above P (since P,R,Q collinear and perpendicular to PM). Angle QMP = 45°, so PQ = 100. Angle RMP = tan⁻¹(50/100) = tan⁻¹(1/2). Angle RMQ = QMP - RMP = 45° - tan⁻¹(1/2). Using tan(RMQ) = (1 - 1/2)/(1 + 1·1/2) = (1/2)/(3/2) = 1/3. So angle RMQ = tan⁻¹(1/3).
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