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.