A man wishes to find the height of a flagspost which stands on a horizontal plane, at a point on this plane he finds the angle of elevation of the top of the flagspost to be θ_{1}. On walking 'z' units towards the tower he finds the corresponding angle of elevation to be θ_{2}. Then the height (H) of the flagpost is given by
[
ztanθ_{1}tanθ_{2}
/
tanθ_{2} − tanθ_{1}
] units and the value of DB(below given) is given by
ztanθ_{1}
/
tanθ_{2} − tanθ_{1}
units.
z = 100
θ_{1} = 30°
θ_{2} = 45°
Height = ?
Using these values in the shortcut, we get:
H =
100 x 1/√3 x 1
/
1 − 1/√3
H =
100 x 1/√3 x 1
/
(√3 − 1)/√3
H =
100
/
(√3 − 1)
H =
100(√3 + 1)
/
(√3 − 1)(√3 + 1)
H =
100(√3 + 1)
/
3 − 1
H =
100(√3 + 1)
/
2
= 50(√3 + 1)
Hence, the height of the light house is 50(√3 + 1) metres.
