Math, asked by estephanielopez40, 1 year ago

why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

Answers

Answered by nyp623
22

Answer:

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.

Step-by-step explanation:

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Answered by sadiaanam
0

Answer: In a right triangle, the sine ratio of an acute angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse of the triangle. This ratio is denoted by sinθ, where θ is the measure of the angle in degrees or radians.

Step-by-step explanation:

The sine ratio for an acute angle of a right triangle must always be a positive value less than 1 because of the following reasons:

  • In a right triangle, the hypotenuse is always the longest side, and the side opposite to an acute angle is always shorter than the hypotenuse. Therefore, the ratio of the length of the opposite side to the hypotenuse is always less than 1.
  • Since the angle is acute, it lies between 0 and 90 degrees. In this range, the sine function is always positive. Therefore, the sine ratio of an acute angle in a right triangle is always positive.
  • The value of the sine ratio depends on the ratio of the lengths of two sides of the triangle. Since the opposite side is always shorter than the hypotenuse, the sine ratio is always less than or equal to 1.
  • However, it cannot be greater than 1, as this would imply that the opposite side is longer than the hypotenuse, which is not possible in a right triangle.

Hence, the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

Learn more about right triangle :

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