An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 45° and 60 respectively, Find the width of the river Write the answer correct to the nearest whole number. (2014)
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Answer:
Step-by-step explanation:
Let AD=250 m, height of aeroplane
Two boats are at B and C.
Let BD=x and DC=y
From △ADB,
250
x
=cot45
∘
250
x
=1
⇒x=250 m
From △ADC,
250
y
=cot60
∘
250
y
=
3
1
⇒y=250×
3
1
Width of river BC=BD+DC=x+y
=250+
3
250
=250(1+
3
1
)=250(
3
3
+1
)
=250(
1.732
1.732+1
)=250(
1.732
2.732
)
=250×1.577
=394.25 m≈394 m.
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