The sine of angle a can be expressed as a ratio in simplest form as follows:
sin a = opposite / hypotenuse
In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse (the longest side of the triangle). For example, if the length of the side opposite the angle a is 3 units and the length of the hypotenuse is 5 units, then:
sin a = 3 / 5
This fraction represents the sine of angle a in its simplest form. Always remember that this ratio is only applicable for angles within a right triangle.