Multiple choice

If angle $A$ is acute and $\cos A= \displaystyle\frac{8}{17}$, then $\cot A$ is

  1. $\displaystyle\frac{8}{15}$
  2. $\displaystyle\frac{17}{8}$
  3. $\displaystyle\frac{15}{8}$
  4. $\displaystyle\frac{17}{15}$
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A Correct answer
Explanation

If cos A = 8/17, then in a right triangle, adjacent = 8 and hypotenuse = 17. Using Pythagoras, opposite = sqrt(17^2 - 8^2) = sqrt(289 - 64) = sqrt(225) = 15. Cot A = adjacent / opposite = 8/15.

AI explanation

Using the Pythagorean identity, sin squared A plus cos squared A equals 1, we find sin A equals root of 1 minus 64 over 289, which is 15 over 17. The cotangent ratio is defined as cos A divided by sin A. Substituting the values gives 8 over 17 divided by 15 over 17, resulting in 8 over 15.

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