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.

The sine of an angle x is defined as the ratio of the opposing side to the hypotenuse, in a right triangle having x as one of its acute angles. If it was greater than 1, it would mean the opposing side was longer than the hypotenuse. Try to draw a right triangle with one of the sides longer than the diagonal. You'll notice it's impossible. So the sine cannot be greater than 1. 

Fitting the triangle into a circle of radius 1, such that the angle x is located at the origin and the hypotenuse is a radius of the circle, you can define "sine of x" for any angle. Since the triangle may end up flipped in any direction, including the negative x and y axis, it turns out that the sine of any number is between -1 and +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.

For more information please refer to the link below

link

A. but. i don’t nohxbzbz