| 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: |
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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