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Question

A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30o. A girl standing on the roof of 20 m high building, finds the angle of elevation of the same bird to be 45o. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girls.

A
44.62 m
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B
52.35 m
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C
36.92 m
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D
42.42 m
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Solution

The correct option is D 42.42 m
The position of the boy is at point B of elevation 30o and that of the girl is at point G of elevation 45o.

In PQB
sin 30o=PQPB

=>12=PQ100

=>PQ=50 m
Now,
PS=PQSQ
=PQGR
=(5020) m
=30 m
In PSG
sin45o=PSPG

=>12=30PG
=>PG=302 m
=>PG=3×1.41429 [since 2=1.41429]
=>PG=42.42
The distance of the bird from the girls is 42.42 m

406668_237035_ans_db1a37f8f9404d93b524c7a236489c5f.png

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