Question

1. what is the tangent ratio of angle θ within a right triangle?

○ tanθ = adjacent/opposite
○ tanθ = opposite/hypotenuse
○ tanθ = adjacent/hypotenuse
○ tanθ = opposite/adjacent

Explanation:

In a right triangle, the tangent of an acute angle \( \theta \) is defined as the ratio of the length of the opposite side to the length of the adjacent side. So we check each option:

• The first option has adjacent over opposite, which is incorrect.
• The second option has opposite over hypotenuse, which is sine, not tangent.
• The third option has adjacent over hypotenuse, which is cosine, not tangent.
• The fourth option has opposite over adjacent, which matches the definition of tangent.

Answer:

D. \( \tan\theta = \frac{\text{opposite}}{\text{adjacent}} \) (assuming the fourth option is labeled D; if the original options had different labels, adjust the label accordingly, but the formula is \( \tan\theta = \frac{\text{opposite}}{\text{adjacent}} \))