= (64.2199+0.9094)  x Tan⁡〖(100° 21' 50.62")/2〗+18.6944

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.

(64.2199 + 0.9094) x Tan⁡〖(100° 21' 50.62")/2〗 + 18.6944

Learn how to solve the trigonometric expression (64.2199 + 0.9094) x Tan⁡〖(100° 21' 50.62")/2〗 + 18.6944 with a detailed step-by-step explanation. This problem involves angle conversion from degrees, minutes, and seconds (DMS) to decimal degrees and applies the tangent function. Suitable for students in Grades 10-12.

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