Mathematics

Problem

At a point

P

on level ground, the angle of elevation of the top of a lamp post is

30^\circ

. After moving

20\,\text{m}

towards the lamp post to a point

Q

, the angle of elevation becomes

60^\circ

. a. (i) Taking the height of the lamp post to be

h\,\text{m}

and the initial horizontal distance

PD

(from

P

to the foot

D

of the lamp post) to be

x\,\text{m}

, write two equations involving

h

and

x

using the given information. b. (ii) Solve the equations simultaneously to find the height

h

of the lamp post. c. (iii) Find the initial distance

PD

of point

P

from the foot of the lamp post.