We can break down the given expression step by step for clarity:

The expression is:

$(64.2199 + 0.9094) \times \tan \left( \frac{100^\circ 21' 50.62"}{2} \right) + 18.6944$

Step-by-Step Solution:

1. Add the numbers inside the parentheses: $64.2199 + 0.9094 = 65.1293$

2. Convert the angle $100^\circ 21' 50.62"$ to decimal degrees: $100^\circ + \frac{21'}{60} + \frac{50.62"}{3600} = 100^\circ + 0.35^\circ + 0.014061^\circ = 100.364061^\circ$

3. Divide the angle by 2: $\frac{100.364061^\circ}{2} = 50.1820305^\circ$

4. Find the tangent of $50.1820305^\circ$: $\tan(50.1820305^\circ) \approx 1.1985$

5. Multiply the result of the tangent by 65.1293: $65.1293 \times 1.1985 = 78.0491$

6. Add 18.6944 to the result: $78.0491 + 18.6944 = 96.7435$

Final Answer:

$96.7435$

Let me know if you'd like a detailed explanation on any step or have any further questions!

---

Here are five related questions:

1. How do you convert degrees, minutes, and seconds to decimal degrees?
2. What is the significance of using the tangent function in trigonometry?
3. How does the value of $\tan(\theta)$ change as $\theta$ increases from 0° to 90°?
4. What are the practical applications of working with angles in degrees, minutes, and seconds?
5. Can you explain why trigonometric functions are periodic?

Tip: Always ensure your calculator is in degree mode when working with angles in degrees to avoid errors.