Distance between Two Points on the Same Coordinate Axes
From the top ...
Question
From the top of a tower, 80 m high, the angles of depression of two points P and Q in the same vertical plane with the tower are 45∘ and 75∘ respectively, find the value of PQ.
[Use tan75∘=2+√3]
A
80(√3+1) m
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B
80(√3−1) m
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C
160(√3+1) m
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D
160(√3−1) m
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Solution
The correct option is B80(√3−1) m
Let the distance of point Q from the base of the tower be y and distance of point P from Q be x.
In △QSR,
tan75∘=SRy
⇒(2+√3)=80y
⇒y=80(2+√3)
Now, in △PSR,
tan45∘=SRx+y=1=80x+yx+y=80x+802+√3=80x=80−802+√3=80(√3+1)√3+2=80(√3−1) m