Question

an aeroplane at an altitude of 100m observes the angles of depression of two opposite points on two banks of the river to be 45 and 60 find in meters the width of the river

Answer 1

✯ 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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