In right triangle $\triangle{JKL}$, the right angle is at $K$, the length of $\overline{JK}$ is 10 cm, and $\sin{L} = \dfrac{5}{11}$. What is the value of $\cos{J}$ ?

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In a right triangle, the sine of one acute angle is always equal to the cosine of the other acute angle.

The identity is:

$$\sin{\alpha} = \cos{\beta} \text{ if } \alpha + \beta = 90$$ $$\sin{\alpha} = \cos{(90-\alpha)}$$

Sketch a picture of the triangle where $\sin{L}=\dfrac{5}{11}$:

We can see that the cosine of $J$ is the same value.