Question

In a right triangle $ABC$, right-angled at $A$, if $\cos B = \frac{1}{4}$, then the value of $\cot B$ is:

Accepted Answer

B. Since $\cos B = \frac{1}{4} = \frac{	ext{Adjacent}}{	ext{Hypotenuse}}$, let adjacent $= 1$ and hypotenuse $= 4$. $	ext{Opposite} = \sqrt{4^2 - 1^2} = \sqrt{15}$. $$\cot B = \frac{	ext{Adjacent}}{	ext{Opposite}} = \frac{1}{\sqrt{15}}$$

Cotangent value from cosine in right triangle

Explanation

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