https://r2.erweima.ai/mathbot/image/1726360780272b50dmk6i.jpg

We are given:

\[
\text{If} \ \tan(21^\circ) = a,
\]
and we need to compute:

\[
\tan(55^\circ 30') - \tan(34^\circ 30').
\]

### Step 1: Express the angles in decimal form
- \( 55^\circ 30' = 55.5^\circ \)
- \( 34^\circ 30' = 34.5^\circ \)

### Step 2: Find the values of the tangents
We will now use a calculator to find the approximate values for the tangent of these angles:
- \( \tan(55.5^\circ) \)
- \( \tan(34.5^\circ) \)

Let me calculate these values.We have the following values:

- \( \tan(55^\circ 30') \approx 1.455 \)
- \( \tan(34^\circ 30') \approx 0.687 \)
- The difference \( \tan(55^\circ 30') - \tan(34^\circ 30') \approx 0.768 \)
- \( \tan(21^\circ) \approx 0.384 \), which is equal to \( a \).

Thus, the difference \( \tan(55^\circ 30') - \tan(34^\circ 30') \) in terms of \( a \) is:

\[
\frac{0.768}{0.384} = 2a
\]

### Conclusion:
The correct answer is \( \boxed{2a} \), which corresponds to option **c)**.

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Do you have any questions, or would you like more details?

Here are 5 related questions to expand on this topic:
1. How do you compute the tangent of an angle?
2. What is the significance of converting degrees and minutes to decimal form?
3. Can the tangent difference be calculated without a calculator?
4. How do other trigonometric identities (like sine or cosine) relate to tangent?
5. How do we use the tangent subtraction formula in trigonometry?

**Tip**: Always ensure your calculator is in degree mode when working with trigonometric functions for degrees.

If Tg21° = a, Calculate: Tg55°30' - Tg34°30'

Learn how to calculate the difference between Tg55°30' and Tg34°30' when Tg21° is given as 'a'. This problem involves converting degrees and minutes into decimal form, applying the tangent function, and performing subtraction to express the answer in terms of 'a'. Suitable for students in Grades 10-12.

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