A straight pillar stands at a point , the points and are situated due south and east of respectively. is the mid-point of . is an equilateral triangle and is the foot of the perpendicular from on . Suppose and the angle of elevation of the top of the pillar at is . Find the sum of the angles of elevation of its top at and .
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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