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10th
Maths
Some Applications of Trigonometry
Heights and Distances
The angle of elevation thet...
MATHS
The angle of elevation θ of a vertical tower from a point A on the ground is such that its tangent is
12
5
. On walking 192 m towards tower in the same straight line, the tangent of the angle of elevation ϕ formed to be
4
3
. The height of the tower is
HARD
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ANSWER
Let the height of the tower be h.
Let the distance between the foot of the tower and the point till which the man walks 192m be y.
Hence
tanθ=
192+y
h
=
12
5
12h=960+5y ..(i)
tan(ϕ)=
y
h
=
4
3
4h=3y ...(ii)
Substituting in i, we get
9y=960+5y
4y=960
y=240 m
Hence h=
4
3
×240
=180 m
solution