Question

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

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer: See below.

The sine ratio is the ratio of the opposite side over the hypotenuse in a right triangle. The hypotenuse is always the largest side of a triangle.

Therefore, the denominator will always be the largest. If the denominator is larger than the numerator, it will be a number less than one.

And it will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.