Question

A vertical tower PQ stands at a point P. Points A and B are located to the South and East of P respectively. M is the mid point of AB. PAM is an equilateral triangle and N is the foot of the perpendicular from P on AB. Let AN = 20 m and the angle of elevation of the top of the tower at N is tan^-1 (2). Determine the height of the tower and the angles of elevation of the fop of the tower at A and B.

Answer 1

PQ is a tower. The points A and B are respectively due South and due East of the point P so that ∠APB =90°. M is the mid point of AB and N is the foot of perpendicular from P on AB where AN = 20m. N is mid point of AM as ΔPAM is equilateral.

To find the elevations of A and B we first find PA and PB.

PA = AM = 40 by Eq. (i) as ΔPAM is equilateral.