A) \[\frac{d\tan x\tan y}{\tan y-\tan x}\]
B) \[d(\tan y+\tan x)\]
C) \[d(\tan y-\tan x)\]
D) \[\frac{d\tan x\tan y}{\tan y+\tan x}\]
Correct Answer: A
Solution :
Let height of the tower, \[AB=h,\] From \[\Delta \,ADB,\,\tan y=\frac{h}{BD}\] or \[BD=h\,\cot \,y\] From \[\Delta \,ADB\] and ACB, \[\tan x=\frac{h}{d+DB}\] or \[d+DB=h\,\cot \,x\] or \[h(\cot \,x-\,\cot \,y)=d\] \[\therefore \] \[h=\frac{d}{\cot \,c-\cot \,y}\] \[=\frac{d}{\frac{1}{\tan x}-\frac{1}{\tan y}}=\frac{d\,\tan x.\,\tan \,y}{\tan y-\tan x}\]You need to login to perform this action.
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