Question

What is the maximum possible value of a sine ratio? In two or more complete sentences, explain your answer.

Answer 1

Answer:

1

Step-by-step explanation:

The maximum possible value of a sine ratio is 1. This is because the formula to figuring out the sine is opposite leg/hypotenuse. Since the hypotenuse of a triangle is ALWAYS the longest side of the triangle, and it's the denominator of the formula, then the value of a sine ratio will never exceed 1.  

Examples:  (Bold = hypotenuse)

3/5 = 0.6

6/8 = 0.75

If there would be a leg longer than the hypotenuse (which is not possible), then the answers would be greater than 1:

5/3 = 1.666666667

8/6 = 1.333333333

Hope this helps!

Answer 2

The sine ratio is basically a fraction of the opposite side over the hypotenuse. Since the hypotenuse is always the longest side, this means the fraction cannot exceed 1. If it did,then that would lead to the opposite side being larger than the hypotenuse but again the hypotenuse is the longest side. The largest the sine ratio can get is 1.