10th Class Mathematics Introduction to Trigonometry Question Bank Case Based (MCQs) - Introduction to Trigonometry

  • question_answer
    Direction: Q. 1 to 5
    Anika is studying in X standard. She is making a figure to understand trigonometric ratio shown as below.                      
    In \[\Delta PQR,\] \[\angle Q\] is right angled, \[\Delta QTR\]is right angled at T and \[\Delta QST\] is right angled at S. \[PQ=12cm,\] \[QR=8.5cm,\] \[\text{ST}=\text{4 cm},\] \[\text{SQ}=5\text{ cm},\] \[\angle QTS=x{}^\circ \]and\[\angle TPQ=y{}^\circ \]. Give answers to her questions by looking at the figure.                 
    Based on the above information give the answer of the following questions:
    The length of PT is:

    A) \[8\, cm\]

    B) \[\sqrt{65}\,cm\]

    C) \[7.5\,cm\]

    D) \[\sqrt{69}\,cm\]

    Correct Answer: B

    Solution :

    We have, \[PS=PQ-SQ=12-5=7cm\]
    In right \[\Delta PST,\]
    \[{{(PT)}^{2}}={{(PS)}^{2}}+{{(ST)}^{2}}\]   (By Pythagoras theorem)
    \[={{(7)}^{2}}+{{(4)}^{2}}=49+16=65\Rightarrow PT=\sqrt{65}cm\]
    So, option [b] is correct.

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