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Geometry Level 4

A straight pillar P Q PQ stands at a point P P , the points A A and B B are situated due south and east of P P respectively. M M is the mid-point of A B AB . P A M PAM is an equilateral triangle and N N is the foot of the perpendicular from P P on A B AB . Suppose A N = 20 meters AN = 20 \text{ meters} and the angle of elevation of the top of the pillar at N N is tan 1 ( 2 ) \tan^{-1} (2) . Find the sum of the angles of elevation of its top at A A and B B .

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Inspired by IIT 1990 Question.


The answer is 105.

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1 solution

Jomerson Salazar
Mar 2, 2015

PN = 20sqrt(3). PQ is then 40sqrt(3)

Also, PA = 40 and PB = 40sqrt(3). Therefore, angle QAP is 60 degrees and angle QBP is 45 degrees. 60 + 45 = 105

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