A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is `60^0dot` When he retreates 20m from the bank, he finds the angle to be `30^0dot` Find the height of the tree and the breadth of the river.

Explanation

Let {AB} be the breadth of the river and {BC} be the height of the tree which makes a angle of `60^{circ}` at a point A on the opposite bank.

Let {D} be the position of the person after retreating 20 {~m} from the bank.

Let {AB}={x} metres and {BC}={h} metres.

It is known that , `tan (theta)= (Opposite) / (Adjacent)`

From right angle ed triangle {ABC} and {DBC},

we have `tan 60^{circ}=frac{{BC}}{{AB}}` and `tan 30^{circ}=frac{{h}}{20+{x}}`


`Rightarrow sqrt{3}=frac{h}{x}` { and } `frac{1}{sqrt{3}}=frac{h}{x+20}`

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