so CSC is 1/sin so if csc=8/7 that means sin=7/8
sin is opposite over hypotenuse so we have opposite is 7 and hypotenuse is 8
so
[tex] {7}^{2} + {x}^{2} = {8}^{2} \\ 49 + {x}^{2} = 64 \\ {x}^{2} = 15 \\ x = \sqrt{15} [/tex]
so we have an adjacent side of root 15 so cut is equal to cos/sin or 1/tan. so we get.
[tex] \cot(x) = \frac{ \frac{ \sqrt{15} }{8} }{ \frac{7}{8} } = \frac{ \sqrt{15} }{7} [/tex]
