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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