Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60o. when he moves 40 meters away from the bank, he finds the angle of elevation to be 30o. find the height of the tree and the width of the river.

Answer 1

let the distance between the man's initial position and the tree be x
let height of tree be h
applying tan theta = h/x
tan 60° = root 3 = h/x
h= root3x
now applying tan 30°=h/40+x Meyers
tan30°=1/root3x
1/root3= h/40+x
h=40+x/root3
now we know h=root3x =40+x/root3
root3×root3x= 40+x
3x-x=40
2x=40x
now x= 20
h= root3×x
h=20 root3 meters

Answer 2

this is the answer of ur question