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:

The sine of an acute angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In any right triangle, the hypotenuse is the side opposite the 90-degree angle, making it the longest side. Because the side opposite an acute angle must be shorter than the hypotenuse, the numerator of the sine ratio is always smaller than the denominator. Therefore, the ratio must be a positive number less than 1.