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 defined as the length of the opposite side divided by the length of the hypotenuse, both of which are positive. Since dividing a positive number by a positive number results in a positive number, the sine must be positive.

Also, since the hypotenuse is the longest side of the triangle, the sine is equal to some positive number less than the length of the hypotenuse being divided by the length of the hypotenuse, resulting in a number less than 1.