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.? ​

Answer 1

EXPLANATION.

→ Let AD be the height of the aeroplane.

→ BC is the width of the river.

→ AD = 200 m.

→ In ∆ABD

→ Tan ø = P/B = perpendicular/Base.

→ Tan 45° = AD/BD

→ 1 = AD/BD

→ AD = BD

→ AD = 200 M.

→ In ∆ACD

→ Tan ø = P/B = Perpendicular/Base.

→ Tan 60° = AC/CD

→ AC/CD = √3

→ CD = AC/√3

→ Width of the river = BC = BD + DC.

→ 200 + 200/√3

→ 315.4 M.

→ Width of the river = 315.4 M

Answer 2

Answer:

✯ 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,

⇒tan45° = $\dfrac{AD}{BD}$

⇒ 1 = $\dfrac{AD}{BD}$

⇒ AD = BD

⇒ BD = 200 m

Again,

➟ In ∆ACD

⇒ tan60° = $\dfrac{AC}{CD}$

⇒ √3 = $\dfrac{AC}{CD}$

⇒ CD = $\dfrac{AC}{√3}$

⇒CD = $\dfrac{200}{√3}$

⇒ BC = BD + CD

⇒ BC = 200 + $\dfrac{200}{√3}$

➥ BC = 315.4 m

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

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