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Let's work through the table by calculating the missing values based on the given information. Here’s a breakdown of what each term represents:

1. **Slope**: Slope is defined as \( \text{slope} = \frac{\text{rise}}{\text{run}} \), and it can also be calculated as \( \tan(\text{angle of elevation}) \).
2. **Angle of Elevation**: The angle made by the line of sight above the horizontal.
3. **Rise**: The vertical distance.
4. **Run**: The horizontal distance.

I'll start filling out the table based on these relationships:

### First Row:
- **Slope**: \(\tan(65^\circ)\)
    - Using a calculator, \( \tan(65^\circ) \approx 2.1445 \).
- **Run**: 34 is given.
- **Rise**: From the slope formula, \( \text{Rise} = \text{slope} \times \text{run} \). Thus, \( \text{Rise} = 2.1445 \times 34 \approx 72.9 \).

### Second Row:
- **Rise**: 24 is given.
- **Run**: 10 is given.
- **Slope**: \( \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{24}{10} = 2.4 \).
- **Angle of Elevation**: \( \tan^{-1}(2.4) \approx 67.4^\circ \).

### Third Row:
- **Slope**: 1.98 is given.
- **Run**: Let's assume the missing value is the run.
- **Rise**: 15 is given.
- From the slope formula, \( \text{Run} = \frac{\text{Rise}}{\text{Slope}} = \frac{15}{1.98} \approx 7.6 \).
- **Angle of Elevation**: \( \tan^{-1}(1.98) \approx 63.5^\circ \).

Here’s the updated table:

| Slope          | Angle of Elevation | Rise  | Run   |
|----------------|--------------------|-------|-------|
| 2.1445         | 65°                | 72.9  | 34    |
| 2.4            | 67.4°              | 24    | 10    |
| 1.98           | 63.5°              | 15    | 7.6   |

Would you like me to explain any specific part of the calculations, or do you need further details?

### Follow-up Questions:
1. What is the relationship between slope and the tangent of an angle?
2. How would you calculate the rise if only slope and run are given?
3. Can you explain why the tangent function is used to find slope in these problems?
4. How can you determine the angle of elevation given the rise and run?
5. What happens to the angle of elevation as the slope increases?

**Tip**: Always use inverse trigonometric functions carefully when calculating angles from slopes.

Complete the following chart. Round angles to the nearest degree and measurements to the nearest tenth of a unit.

Learn how to calculate slope, angle of elevation, rise, and run using trigonometric functions like the tangent. This example provides step-by-step solutions, ideal for Grades 10-12 math students.

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