Question : If 3 cot A = 4 and A is an acute angle, then find the value of sec A.
Option 1: $\frac{3}{4}$
Option 2: $\frac{5}{4}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{5}{3}$
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Correct Answer: $\frac{5}{4}$
Solution :
Given: 3 cot A = 4
⇒ cot A = $\frac{4}{3}=\frac{\text{Base}}{\text{Perpendicular}}$
Let Base = 4k and Perpendicular = 3k
So, Hypotenuse = $\sqrt{{3k}^2+{4k}^2} = 5k$
$\therefore$ sec A = $\frac{\text{Hypotenuse}}{\text{Base}}=\frac{5k}{4k}=\frac{5}{4}$
Hence, the correct answer is $\frac{5}{4}$.
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