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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.

Respuesta :

The triangle is given to be a right angled triangle. This means one of the angles will be 90 degree.

Remember that the sum of all 3 angles of a triangle is always equal to 180 degrees. So, if one angle is 90 degree, this means the sum of remaining two angles will be 90 degree. Or in other words, we can write the remaining two angles will have a value less than 90 and greater than 0.

Sine ratio of angles less than 90 and greater than 0 will always be a positive values less than 1.

Sin(90) = 1 and Sin(0) = 0

And Sine ratio of any angle between 0 and 90 will always be between 0 and 1
kaliyahgutierre

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.

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