Question

Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

Answer 1

The sine is the opposite side  / hypotenuse and the hypotenuse is the longest side.  So the ratio must be  less than 1,  and as the lengths  are positive the sine must be positive.

Answer 2

The sine ratio is the length of the side opposite a given acute angle divided by the length of the hypotenuse. Because the hypotenuse is the side opposite the largest angle, the 90° angle, it has to be the longest side. Thus, the ratio will have a denominator that is larger than the numerator, and the ratio will be less than 1.