sin θ = opposite leg/hypotenuse
csc θ = hypotenuse /opposite leg =8/7
cot θ = adjacent leg/opposite leg
hypotenuse =8
opposite leg =7
We need to find adjacent leg.
(Opposite leg)² +(adjacent leg)² = hypotenuse²
7² + (adjacent leg)² =8²
(adjacent leg)² = 64 - 49
(adjacent leg)² = 15
adjacent leg=+/-√15
WE need only positive root,
so adjacent leg =√15
cot θ = √15/7 or 0.5533