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.
Note: The angle of elevation of a lampost changes from θ_{1} to θ_{2}, when a man walks towards it. If the height of the lampost is H metres, then the distance travelled by man is given by
[
H(tanθ_{2} − tanθ_{1})
/
tanθ_{1} x tanθ_{2}
] metres.
2. If the time for which man walks towards lampost is given as 't' see then speed of the man can be calculated by the formula given below.
Speed of the man = [
H
/
t
x
(tanθ_{2} − tanθ_{1})
/
tanθ_{1} x tanθ_{2}
]
z = 20
θ_{1} = 30°
θ_{2} = 60°
Using these values in the shortcut, we get:
= [
20 x tan60° x tan30°
/
tan60° − tan30°
]
= [
20 x √3 x 1/√3
/
√3 − 1/√3
]
= [
20 x √3
/
√3 x √3 − 1
]
= [
20√3
/
3 − 1
]
= [
20√3
/
2
]
= 10 x 1.732 = 17.32
