JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Relation between sides and angles, Solutions of triangles

  • question_answer
    In a \[\Delta ABC\], if \[\angle C={{30}^{o}}\], \[a=47cm\]and \[b=94\]cm, then the triangle is [MP PET 1986]

    A) Right angled

    B) Right angled isosceles

    C) Isosceles

    D) Obtuse angled

    Correct Answer: D

    Solution :

    \[\cos C=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}\] Þ \[\frac{\sqrt{3}}{2}=\frac{{{(47)}^{2}}+{{(94)}^{2}}-{{c}^{2}}}{2\times 47\times 94}\]\[\Rightarrow c=58.24\] \[\angle B={{124}^{o}}\]. Hence obtuse angled triangle.


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