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 = ?
θ_{1} = 45°
θ_{2} = 60°
Height = 1200
Using these values in the shortcut, we get:
1200 =
z x tan60° x tan45°
/
tan60° − tan45°
z = 1200[
tan60° − tan45°
/
tan60° x tan45°
]
z = 1200[
√3 − 1
/
√3 x 1
]
z = 1200[
√3 − 1
/
√3
]
z = 1200[ 1 −
1
/
√3
]
z = 1200 −
1200 x √3
/
√3 x √3
z = 1200 −1200(
√3
/
3
)
z = 1200 − 400√3
z = [1200 − (400 x 1.732)] = 507.2
Hence, the distance between the two ships is 507.2 metres.
