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

  • question_answer
    Two straight roads intersect at an angle of\[{{60}^{o}}\]. A bus on one road is 2 km away from the intersection and a car on the other road is 3 km away from the intersection. Then the direct distance between the two vehicles is  [BIT Ranchi 1993]

    A) 1 km

    B) \[\sqrt{2}\,\,km\]

    C) 4 km

    D) \[\sqrt{7}\,\,km\]

    Correct Answer: D

    Solution :

    Let the two roads intersect at \[A\]. If the bus and the car are at \[{{a}^{2}}+{{b}^{2}}=8{{p}^{2}}\] and \[C\] on the two roads respectively, then \[c=AB=2km,\,b=AC=3\] km. The distance between the two vehicles = \[BC=a\text{ }km\] Now \[\cos A=\cos {{60}^{o}}=\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc}\] \[\Rightarrow \] \[\frac{1}{2}=\frac{{{3}^{2}}+{{2}^{2}}-{{a}^{2}}}{2\,.\,3.\,2}\Rightarrow a=\sqrt{7}\,\,km.\]

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