$\operatorname{cosec}\theta = \dfrac{\text{hypotenuse}}{?}$

Since $\operatorname{cosec}\theta=\dfrac{1}{\sin\theta}$ and $\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}}$, taking the reciprocal gives $\operatorname{cosec}\theta=\dfrac{\text{hypotenuse}}{\text{opposite}}$. The denominator is therefore the opposite side.