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 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.

The sine angle is always less than 1 because the ratio of opposite side to the hypothenuse side is always less than 1

Data;

  • sine angle
  • opposite
  • hypothenuse

Sine Angle in a Right-Angle Triangle

The sine angle in a right angle triangle is calculated by the ratio between the opposite to the hypothenuse.

The reason why it is always less than 1 is because the longest side in a right angle triangle is the hypothenuse and hence dividing the opposite side by the hypothenuse will always be less than 1

mathematically;

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