Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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What does the cosine ratio represent in a right triangle?

  1. Opposite ÷ Adjacent

  2. Adjacent ÷ Hypotenuse

  3. Hypotenuse ÷ Adjacent

  4. Opposite ÷ Hypotenuse

The correct answer is: Adjacent ÷ Hypotenuse

In a right triangle, the cosine ratio specifically represents the relationship between the adjacent side and the hypotenuse. The cosine of an angle in a right triangle is defined as the length of the side that is adjacent to the angle divided by the length of the hypotenuse, which is the longest side of the triangle opposite the right angle. This relationship is crucial in trigonometry and is widely used in various applications, such as physics and engineering, to find distances and angles. Understanding why the cosine ratio is defined this way helps deepen comprehension of the triangle's geometric properties and its angles. By knowing the cosine of an angle, you can easily calculate the length of sides related to that angle when you have one of the sides already known. This capability is essential for solving many problems involving right triangles.

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