Which triogonometric ratio related the adjacent side and opposite side of the right-angled triangle?

Options

A. `sintheta`
B. `costheta`
C. `tantheta`
D. `sectheta`

Answer

To solve the question "Which trigonometric ratio relates the adjacent side and opposite side of the right-angled triangle?", we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Right-Angled Triangle**:
- Consider a right-angled triangle ABC, where angle B is the right angle. Let angle A be θ (theta).

2. **Identify the Sides**:
- In the triangle, the side opposite angle θ (A) is called the opposite side, which we can denote as \( AB \).
- The side adjacent to angle θ (A) is called the adjacent side, which we can denote as \( BC \).

3. **Recall the Trigonometric Ratios**:
- The primary trigonometric ratios are:
- Sine (sin): \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \)
- Cosine (cos): \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
- Tangent (tan): \( \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \)

4. **Determine the Ratio of Opposite to Adjacent**:
- The ratio that relates the opposite side \( AB \) to the adjacent side \( BC \) is given by the tangent function.
- Thus, we have:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{AB}{BC} \]

5. **Conclusion**:
- Therefore, the trigonometric ratio that relates the adjacent side and opposite side of a right-angled triangle is the tangent function, \( \tan(\theta) \).

### Final Answer:
The trigonometric ratio that relates the adjacent side and opposite side of a right-angled triangle is **Tangent (tan)**.

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