$$ \text{ \small {Note: Figure not drawn to scale.}} $$

In the figure above, \( \cos{(90\degree-x\degree)}=\dfrac{12}{13} \). What is the value of \( \cos{x\degree} \)?

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An angle defined as \( 90 \degree - x\degree\) refers to an angle that is complementary to \(x\degree\). We can identify this on the figure as the other acute angle. We can use the cosine ratio accordingly to find a possible length for the adjacent side and hypotenuse.

We can find the 3^rd side using the pythagorean theorem or identifying the 5-12-13 pythagorean triplet. Based on the figure above,

$$ \cos{x\degree}=\frac{\text{adjacent}}{\text{hypotenuse}} $$ $$ \cos{x\degree}=\frac{5}{13} $$