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Question

An aeroplane at an altitude of 200 m observes the angle of depression of two opposite points on the two banks of a river to be 45o and 60o. Then, the width of the river is _____.

A
4003 m
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B
4003 m
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C
(2002003) m
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D
(200+2003) m
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Solution

The correct option is D (200+2003) m
From the given figure, A is the aeroplane, and B and C
are the two points of the two banks of the river.
AD = height of aeroplane's altitude =200 m

XAB=45oABD=45o {as they are alternate interior angles}

and, Similarily,
YAC = 60o ACD = 60o

Now, In the right-angled triangle ABD

tan45o=ADBD

1=200BD

BD=200 ....(1)

Also,
In the right-angled triangle ADC

tan60o=ADDC

3=200DC

DC=2003 ....(2)
Now as we know Width of the river =BD+DC

From(1)and(2)

BD+DC =(200+2003) m

So, option D is correct.

478504_452864_ans_aa2b98ac43e1416d938e9d8de78403b4.png

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