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ICSE Class X Math 2014 Solved Paper

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Question : 52
Total: 52
An aeroplane at an altitude of 250m 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.
Solution:  
Let AD=250m height of aeroplane
Two boats are at B and C.

Let ‌‌BD=x and DC=y
From △ADB;
‌‌ From ‌△ADB;‌‌
x
250
‌=cot‌45∘
‌
x
250
‌=1
⇒x‌=250m
From △ADC;‌‌‌
y
250
=cot‌60∘
‌
y
250
‌=‌
1
√3
⇒‌‌y‌=250×‌
1
√3
m
Width of river BC=BD+DC
‌=x+y
‌=250+‌
250
√3
‌=250(1+‌
1
√3
)
‌=250(‌
√3+1
√3
)
‌=250(‌
1.732+1
1.732
)=250(‌
2.732
1.732
)
‌=250×1.577
‌=394.25m=394m.
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