If the height of a tower and the distance of the point of observation

from its foot, both, are increased by 20%, then the angle of elevation of
its top remains unchanged.

given: AB be the height of the tower and C be the observation point, 

such that distance of the observation point from its foot be BC.

let the angle of elevation be θ.

.............(1)

if the height of the tower is increased by 20% = 20/100 =1/5

the height of the tower =

if the distance is increased by 20%.

the distance between the observation point and the foot of the tower =

let us take the new angle of elevation be β.

thus the angle of elevation is constant.

if the height of the tower and the distance of the point of observation from its foot is increased by same percentage, the angle remains constant.

hope this helps you.

  • 30

let C be the foot

let the initial observation point be B &

top of the tower be A

let New top be D & new

observation point be E

so according to question

BE=20% of BC

so BE=BC/5

So

CE=6BC/5

similarly 

CD=6CA/5

in triangles

ACB & DCE

AC/CD=BC/BE & angACE=angDCE

so triangles ACB~DCE

so

angABC=angDEC

so angle of elevation is conctant

  • 5
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