Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are 30º and 45º, respectively, at a point on the road between the pillars. What is the difference (in m) of the point from the foot of pillar A?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 20(3 -)
In PDC,
Tan45 = DC/PD
DC = PD = h
PN = 40 - h
In PNM,
Tan30 = MN/NP
1/ = h/(40 - h)
40 - h = h
h = 40/()
h = 20( - 1)
PN = 40 - h = 40 - 20 + 20
PN = 20(3 - ).