Question

an aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. find the width of the river.?
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Answer 1

Answer:

• Let the position of the aeroplane be A, B and C be two points on the two banks of a river such that the angles of depression at B and C are 45° and 60° respectively.
• Let BD = x m, y m andAD = 200 m.
• Hence, the width of the river is 315.4 metres.

Answer 2

Explanation:

ʜᴇy ᴍᴀᴛᴇ ........

$tan \: thetha = \frac{p}{b} = \tan(45) = \frac{y}{200} .......(1) \: eqn \: \\ \\ similarly \\ \\ \tan(30) = \frac{p}{b} = \frac{x}{200} ......(2) \\ \\ 1 = \frac{y}{200} = y = 200 \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{200} = x = \frac{200}{ \sqrt{3} } \\ \\ suppose \: w = x +y \\ \\ = 200 + \frac{200}{ \sqrt{3} } \\ \\ = 200(1 + \frac{1}{ \sqrt{3} } )$

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