Shortcut:
Two poles of equal heights stand on either sides of a roadway which is 'z' units wide. At a point of the roadway between the poles, the elevations of the tops of the pole are θ_{1}° and θ_{2}°, then the
(i) the heights of poles =
ztanθ_{1}tanθ_{2}
/
tanθ_{1} + tanθ_{2}
units
(ii) position of the point P from B(see the figure) =
ztanθ_{2}
/
tanθ_{1} + tanθ_{2}
units.
(iii) position of the point P from D(see the figure) =
ztanθ_{1}
/
tanθ_{1} + tanθ_{2}
units.
Here, θ_{1} = 30°, z = 30, θ_{2} = 60°
Using these values in the shortcut, we get:
Height of the pole =
30 x 1/√3 x √3
/
1/√3 + √3
=
15√3
/
2
= 7.5 x 1732 = 12.975 ≈13
Hence, the height of the pole is 13 metres.
