The top of a hill observed from the top and bottom of a building of height ′h′ is at angles of elevation p and q, respectively. The height of hill
A
hcotqcotq−cotp
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B
hcotpcotp−cotq
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C
htanptanp−tanq
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D
None of these
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Solution
The correct option is Bhcotpcotp−cotq From △ABE BEAB=tanq⇒AB=(h+x)cotq...(1)
From △CDE DECD=tanp⇒CD=xcotp...(2)
From (1) and (2) ⇒(x+h)cotq=xcotp ⇒x=hcotqcotp−cotq ⇒x+h=hcotpcotp−cotq ∴BE=hcotpcotp−cotq