Question : If $\cot A=\frac{12}{5}$, then the value of $\sin A=?$
Option 1: $\frac{5}{13}$
Option 2: $\frac{12}{13}$
Option 3: $\frac{5}{12}$
Option 4: $\frac{13}{12}$
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Correct Answer: $\frac{5}{13}$
Solution :
$\cot A=\frac{12}{5} = \frac{AB}{BC}$
Let $AB$ and $BC$ be 12 units and 5 units respectively.
So, $AC= \sqrt{5^2+12^2} = \sqrt{25+144} = \sqrt{169} = 13$ units
⇒ $\sin A = \frac{BC}{AC} = \frac{5}{13}$
Hence, the correct answer is $\frac{5}{13}$.
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