10th Class Mathematics Triangles Question Bank Triangles

  • question_answer
    In the given figure, two line segments AC and BD intersect each other at point P, such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, \[\angle \text{APB}=\text{5}0{}^\circ \]and \[\angle \text{CDP}=\text{3}0{}^\circ \]. Find\[\angle \text{PBA}\].

    A)  \[\text{7}0{}^\circ \]                                     

    B)  \[\text{8}0{}^\circ \]

    C)  \[\text{9}0{}^\circ \]                                     

    D)  \[\text{1}00{}^\circ \]

    Correct Answer: D

    Solution :

     \[\sqrt{{{15}^{2}}+{{8}^{2}}}=\sqrt{289}=17\,m\] \['x'\] \[{{x}^{2}}={{34}^{2}}-{{16}^{2}}\] \[\Rightarrow \] \[x=\sqrt{{{34}^{2}}-{{16}^{2}}}=30\,m\] \[\Delta \text{ABC}\,\,\text{ }\!\!\tilde{\ }\!\!\text{ }\,\,\Delta \text{DEF}\] \[\frac{area\,of\,\Delta ABC}{area\,of\,\Delta DEF}={{\left( \frac{BC}{DE} \right)}^{2}}\]


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