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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.

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Final answer:

The sine ratio for an acute angle of a right triangle is always a positive value less than 1, determined by the side lengths and properties of right triangles.


Explanation:

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The sine ratio for an acute angle of a right triangle must always be a positive value less than 1 due to the nature of the sine function and the properties of right triangles.

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In a right triangle, the sine ratio of an acute angle is calculated as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

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Since the length of any side of a triangle is always less than or equal to the length of the hypotenuse, the sine ratio for an acute angle will always be a positive value less than 1.


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