If the height of a tower and the distance of the point of observation
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.
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.
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
ACB & DCE
AC/CD=BC/BE & angACE=angDCE
so triangles ACB~DCE
so angle of elevation is conctant