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.

Sine ratio for an acute angle of a right triangle always be a positive value less than 1.

In a right angled Δ ABC, sine of angle   can be written as:

Therefore,

Please refer to the diagram that is uploaded in the solution.

The Pythagoras theorem can be used to determine the unknown value in a right triangle from two known values.

Thus, the formulated way to represent the theorem for hypotenuse is given below:    

Hence,

Hypotenuse is the longest side of the Right  triangle and therefore its value must be greater than zero and should always be more than perpendicular.

Thus,

so, we can say that is always positive and   less then  1.

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answer: the answer is d

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