In a right triangle, the angles are such that one is \(90^\circ\) and the other two are acute angles whose measures add up to \(90^\circ\). If you have an acute angle \(a^\circ\) and you know that \(\sin(a^\circ) = x\), you can find the cosine of the complementary angle, which is \(90^\circ - a^\circ\).
According to the co-function identities in trigonometry, the sine of an angle is equal to the cosine of its complementary angle:
\[ \sin(a^\circ) = \cos(90^\circ - a^\circ) \]
Given that \(\sin(a^\circ) = x\), it follows that:
\[ \cos(90^\circ - a^\circ) = x \]
Thus, if \(\sin(a^\circ) = x\), then:
\[ \cos(90^\circ - a^\circ) = x \]
So the cosine of the angle \(90^\circ - a^\circ\) must also be equal to \(x\).