| Direction: Q. 6 to 10 |
| A sailing boat with triangular masts is shown below. Two right triangles can be observed. Triangles PQR and PQS. both right-angled at Q. The distance \[\text{QR}=\text{2 m}\] and \[\text{QS}=\text{3 m}\] and height \[\text{PQ}=\text{5 m}\]. |
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| Based on the above information, give the answer of the following questions: |
A) \[\frac{\sqrt{34}}{5}\]
B) \[\frac{\sqrt{34}}{3}\]
C) \[\frac{5}{3}\]
D) \[\frac{3}{\sqrt{34}}\]
Correct Answer: B
Solution :
| In right \[\Delta PQS\] |
| \[{{(PS)}^{2}}={{(SQ)}^{2}}+{{(PQ)}^{2}}={{(3)}^{2}}+{{(5)}^{2}}=9+25=34\] |
| (By Pythagoras theorem) |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,PS=\sqrt{34}m\] |
| \[\therefore \] In right \[\Delta PQS\] |
| \[\sec S=\frac{Hypotenuse}{Base}=\frac{PS}{SQ}=\frac{\sqrt{34}}{3}\] |
| So, option [b] is correct. |
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