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

  • question_answer
    If in a triangle \[ABC\]right angled at \[B,s-a=3\], \[s-c=2\], then the values of a and c are respectively

    A) 2, 3

    B) 3, 4

    C) 4, 3

    D) 6, 8

    Correct Answer: B

    Solution :

    \[s-a=3\Rightarrow b+c-a=6\] ....(i) \[s-c=2\Rightarrow a+b-c=4\] ....(ii) Adding these two equations, we get \[b=5\] Since B is a right angle \ \[{{b}^{2}}={{a}^{2}}+{{c}^{2}}\Rightarrow {{a}^{2}}+{{c}^{2}}=25\] ....(iii) Solving, we get \[a=3,c=4\] .


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