In `DeltaCAT, angleA` is a right angle. Which of the following is equal to `tanT`?

Options

A. `(CA)/(CT)`
B. `(CA)/(AT)`
C. `(CT)/(CA)`
D. `(CT)/(AT)`

Answer

To solve the problem, we need to find the value of \( \tan T \) in triangle \( \Delta CAT \), where \( \angle A \) is a right angle.

### Step-by-Step Solution:

1. **Identify the Triangle**:
We have triangle \( CAT \) with \( \angle A \) being the right angle. This means that \( C \) and \( T \) are the other two vertices.

2. **Understand the Definition of Tangent**:
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

3. **Identify the Sides**:
- The side opposite to angle \( T \) is \( CA \) (height).
- The side adjacent to angle \( T \) is \( AT \) (base).

4. **Write the Tangent Ratio**:
Therefore, we can express \( \tan T \) as:
\[ \tan T = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{CA}{AT} \]

5. **Final Expression**:
Thus, the value of \( \tan T \) in triangle \( CAT \) is:
\[ \tan T = \frac{CA}{AT} \]

### Conclusion:
The correct answer is \( \tan T = \frac{CA}{AT} \).