Question : $\triangle{ABC}$ is a right angled triangle. $\angle \mathrm{C}=90°$, AB = 25 cm and BC = 20 cm. What is the value of $\mathrm{sec}\; A$?
Option 1: $\frac{5}{3}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{4}{3}$
Option 4: $\frac{5}{4}$
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Correct Answer: $\frac{5}{3}$
Solution : Given, AB = 25 cm and BC = 20 cm Using the Pythagoras theorem, $AB^2=BC^2+AC^2$ ⇒ $AC^2=25^2-20^2$ ⇒ $AC^2=625-400$ ⇒ $AC^2=225$ ⇒ $AC = 15$ cm We know, $\sec A =\frac{\text{Hypotenuse}}{\text{Base}}$ So, $\sec A = \frac{AB}{AC} = \frac{25}{15}= \frac{5}{3}$ Hence, the correct answer is $\frac{5}{3}$.
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