Question

At a point on level ground, the angle of the elevation of the top of a vertical tower is found to be such that its tangent is 5/12 . On walking 192 meters towards the the tower, the tangent of the new angle of elevation is found to be 3/4.

Find the height of the tower.
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Answer 1

Answer:

tanθ

1

=

OA

OH

=

OA

h

12

5

=

OA

h

OA=

5

12

h

tanθ

2

=

4

3

=

OB

OH

=

OB

h

OB=

3

4

h

∴OA−OB=192

∴(

3

−4

+

5

12

)h=192

h(

15

36−20

)=192

h=192×

16

15

h=15×12

h=180m

Height of tower is 180m