Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which formula represents the tangent ratio?

1. Opposite ÷ Adjacent

2. Adjacent ÷ Hypotenuse

3. Opposite ÷ Hypotenuse

4. Hypotenuse ÷ Opposite

The correct answer is: Opposite ÷ Adjacent

The tangent ratio in trigonometry is defined as the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. This is expressed mathematically as: Tangent (tan) = Opposite / Adjacent This means that when you take the tangent of an angle in a right triangle, you are looking at how tall the triangle is relative to how wide it is. This ratio is particularly useful in various applications such as calculating heights or distances in navigation, surveying, and physics. In contrast, the other options represent different trigonometric ratios. The adjacent divided by the hypotenuse corresponds to the cosine ratio, and the opposite divided by the hypotenuse corresponds to the sine ratio. The last option, hypotenuse divided by opposite, does not correspond to a standard trigonometric function. Each of these represents distinct relationships between the sides of a triangle and is applied in different contexts, but only the opposite over adjacent configuration accurately describes the tangent ratio.