• # 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) $\sqrt{69}\,cm$

 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.