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 metres 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 AB be the tree of height h metres standing on the bank of a river.Let C be the position of man standing on the opposite bank of the river such that BC=x m. Let D be the new position of the man. It is given that CD=40m and the angle of elevation of the top of the tree at C and D are 60º and 30º, respectively,i.e,  

Hence, the height of  the tree is 34.64m and width of the river is 20m.