Question
Download Solution PDFThe distance between two pillars of length 16 m and 9 m is x meters. If two angles of elevation of their respective top from the bottom of the other are complementary to each other, then the value of x in meters is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
The distance between two pillars of length 16 m and 9 m is x meters.
Two angles of elevation of their respective top from the bottom of the other are complementary to each other.
Concept used
If two angles of elevation are complimentary to each other then H = √ab
Where a and b are the Length of the pillars.
Calculation
AB and CD are two pillars of Length 16 m and 9m.
Let the angle of elevation at B and D be θ and (90 - θ)
Distance between two pillars BD be x metres
IN Δ ABD
Tanθ = AB/BD = 16/x - - - -(i)
In Δ BDC
Tan(90 - θ) = CD/BD = 9/x
Cotθ = 9/x - - - - (ii)
Multiply equation i and ii
⇒ Tanθ × Cotθ = (16/x) (9/x)
⇒ 144/x2 = 1
⇒ x2 = 144
⇒ x = 12 m
Alternate MethodIf two angles of elevation are complimentary to each other then x = √ab
Where a and b are the Length of the pillars.
x = \(\sqrt {16 \times 9} \)
x = √144
x = 12 m
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