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A person walking along a canal observes that two objects are i

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A person walking along a canal observes that two objects are in the same line which is inclined at an angle $α$ to the canal. He walks a distance $C$ for the and observes that the objects subtended their greatest angle $β$ then the distance between the object is

\frac{2 C sin α sin β}{cos β - cos α}

\frac{2 C sin α sin β}{cos α - cos β}

\frac{2 C sin α sin β}{cos α + cos β}

\frac{2 C cos α cos β}{sin α - sin β}

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A person walking along a canal observes that two objects are in the same line which is inclined at an angle

α

to the canal. He walks a distance

C

for the and observes that the objects subtended their greatest angle

β

then the distance between the object is

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Text solutionVerified

tan α = \frac{h _{1}}{a} - (1), tan α = \frac{h _{2}}{a + b} - (2), tan β = \frac{h _{1}}{a - c} - (3)

tan β = \frac{h _{2}}{a + b - c} - (4)

tan β (a + b - c) = tan α (a + b)

(From (1) & (3))

tan α a = tan β (a - c)

(From (2) and (4))

a = \frac{tan β c}{tan β - tan α}

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Question Text	A person walking along a canal observes that two objects are in the same line which is inclined at an angle $α$ to the canal. He walks a distance $C$ for the and observes that the objects subtended their greatest angle $β$ then the distance between the object is
Answer Type	Text solution:1
Upvotes	150