Question : $\triangle \mathrm{EFG}$ is a right angled triangle. $\angle \mathrm{F}=90°$, $\mathrm{EF}=10 \mathrm{~cm}$ and $\mathrm{FG}=15 \mathrm{~cm}$. What is the value of cosec $\mathrm{G}$?
Option 1: $\frac{\sqrt{13}}{2}$
Option 2: $\frac{2}{\sqrt{3}}$
Option 3: $\frac{\sqrt{13}}{10}$
Option 4: $\frac{10}{\sqrt{3}}$
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Correct Answer: $\frac{\sqrt{13}}{2}$
Solution : $\angle$F = 90°, EF = 10 cm, FG = 15 cm By Pythagoras theorem, Hypotenuse 2 = Base 2 + Perpendicular 2 EG 2 = EF 2 + FG 2 ⇒ EG 2 = 10 2 + 15 2 ⇒ EG 2 = 100 + 225 ⇒ EG = $\sqrt{325}$ cm cosec $\theta$ = $\frac{\text{Hypotenuse}}{\text{Perpendicular}}$ ⇒ cosec G = $\frac{\sqrt{325}}{10} = \frac{\sqrt{25 \times 13}}{10} = \frac{5\sqrt{13}}{10}$ ⇒ $\frac{\sqrt{13}}{2}$ Hence, the correct answer is $\frac{\sqrt{13}}{2}$.
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