Question

an aeroplane at an altitude of 200m the angle of depression of two opposite pointso two banks of a river to be 45 and 60 degrees. find the width of the river in meters

Answer 1

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Answer 2

✯ Given :-

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 40° and 60° .

✯ To Find :-

What is the width of the river.

✯ Solution :-

» Let, AD be the height of the aeroplane

» And, BC = x be the width of the aeroplane.

⋆ Given that, AD = 200 m

➟ In ∆ABD,

$\tt \ \: {tan45° = \dfrac{AD}{BD}}$

$\implies \: 1 = \dfrac{AD}{BD}$

⇒ AD = BD

⇒ BD = 200 m

Again,

➟ In ∆ACD

$\tt \ \: { \implies \: tan60° = \dfrac{AC}{CD}}$

$\tt \ \: { \implies \: \: \sqrt{3} \: \: = \: \: \frac{ac}{cd} }$

⇒ BC = BD + CD

⇒ BC = 200 + 115.4

➥ BC = 315.4 m

therefore the width of the river is $\boxed{\bold{\small{315.4\: m}}}$

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