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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    The angle of elevation of the top of a tower as observed from a point on the horizontal ground is x. If we move a distance d towards the foot of the tower, the angle of elevation increases to y, then the height of the tower is

    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            \[h(\cot \,x-\,\cot \,y)=d\] \[\therefore \]  \[h=\frac{d}{\cot \,c-\cot \,y}\]                 \[=\frac{d}{\frac{1}{\tan x}-\frac{1}{\tan y}}=\frac{d\,\tan x.\,\tan \,y}{\tan y-\tan x}\]


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