Answer :

The figure is as follows:


In the given figure, AB represents the height of the tree & BC represents the width of the river. The person at the beginning is at point C observing the top of the tree & making an angle of elevation. Moving 40m away again makes an angle of elevation with the top of tree.


ACB and ADB is angle of elevation


ACB = 60°


BC = x


BD = BC + CD


BD = (x + 40) cm


In ABC


ABC = 90°


tan θ = AB / BC


tan 60° = y / x


√3 = y / x


y = √3 x ………….. (i)


In ∆ ADB


ADB = 30°


tan 30° = AB / BD



But y = √3 x



x + 40 = 3x


2x = 40


x = 20 m


Therefore y = √3 × 20


Height of tree = AB = y = 34.6 m


Width of river = 20 m


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