Question

Given the triangle below, which of the following is a correct statement? Right triangle ABC with AB measuring 5, AC measuring 6, and BC measuring 8. cot angle B equals 6 over 5 csc angle C equals 3 over 4 cot angle C equals 8 over 5 csc angle B equals 4 over 3

Answer 1

Drawing a diagram to match this figure, BC would have to be the hypotenuse as it is the longest side of the triangle.  Angle A would have to be the right angle.  
For the first choice, $\cot B = \frac{1}{ \tan B} \\ = \frac {1}{\frac {6}{5}} \\ = 1 \div \frac{6}{5} = \frac{1}{1} \div \frac{6}{5} \\ = \frac{1}{1} * \frac{5}{6} = \frac{5}{6}$.  The first choice is not correct.
The second choice gives us $\csc C= \frac{1}{ \sin C}= \frac{1}{\frac {5}{8}} \\ = 1 \div \frac{5}{8} = \frac{1}{1} \div \frac{5}{8} \\ = \frac{1}{1} * \frac{8}{5} = \frac{8}{5}$.  The second choice is not correct either.
The third choice gives us