Question

Why must 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

Answer:

Because of the range of the sine function.

Step-by-step explanation:

The reason why the value of the sine ratio for an acute angle

of a right triangle must always be a positive value less

than 1 has to do with the the range of the sine function.

The range of the sine function is

$- 1 \leqslant y \leqslant 1$

But in the first quadrant all y-values are positive and acute angles are less than 90°.

Therefore the range will now be 0≤y<1 for acute angles.

Answer 2

Sample Response: 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.

~Notify me if you have questions~

Have a nice day, and I hope this helps!

-- XxFTSxX