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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