At a point on groumd the angle of elevation of vertical tower is 30 degree found yo be tangent is 5/12 on walking 192 toward tower the tangent of elevation is 3/4. Find height of tower
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Answer: 180m
Step-by-step explanation: Let
TR be the tower such that TR=x
P and Q be the point on the ground such that
tanθ=
12
5
and tanα=
4
3
And QR=y
Given
PQ=192m
In right triangle TQR,
tanα=
QR
TR
=
y
x
⇒
4
3
=
y
x
⇒y=
3
4
x...(1)
In right triangle TPR,
tanθ=
PR
TR
⇒
12
5
=
(y+192)
x
⇒x=
12
5
(y+192)...(2)
⇒x=
12
5
(
3
4
x+192)
⇒x=
9
5
x+80
⇒x−
9
5
x=80
⇒
9
4
x=80
⇒x=
4
9
(80)=180
Hence, the height of the tower is 180 m.
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