Solve any two sub-questions:

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 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. (√3 = 1.73)

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