JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Height and Distance

  • question_answer
    The top of a hill observed from the top and bottom of a building of height h is at the angle of elevation p and q respectively. The height of the hills is [UPSEAT 2001; EAMCET 1989]

    A) \[\frac{h\cot q}{\cot q-\cot p}\]

    B) \[\frac{h\cot p}{\cot p-\cot q}\]

    C) \[\frac{h\tan p}{\tan p-\tan q}\]

    D) None of these

    Correct Answer: B

    Solution :

    Let AD be the building of height h and BP be the hill then \[\tan q=\frac{h+x}{y}\] and \[\tan p=\frac{x}{y}\] Þ  \[\,\tan q=\frac{h+x}{x\cot p}\] \[\Rightarrow \,\,x\cot p=(h+x)\cot q\] Þ  \[x=\frac{h\cot q}{\cot p-\cot q}\] Þ  \[h+x=\frac{h\cot p}{\cot p-\cot q}\].

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