To compute the expression \(\frac{2.1}{\tan(69^\circ)}\), we need to find the value of \(\tan(69^\circ)\) first.

### Step-by-Step Solution

1. The tangent of an angle is defined as:

\[
\tan(69^\circ) = \frac{\sin(69^\circ)}{\cos(69^\circ)}
\]

2. The approximate value of \(\tan(69^\circ)\) is about \(2.6051\).

3. Now, compute:

\[
\frac{2.1}{\tan(69^\circ)} = \frac{2.1}{2.6051}
\]

Let's calculate this value.The value of the expression \(\frac{2.1}{\tan(69^\circ)}\) is approximately \(0.806\).

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. What are some ways to calculate trigonometric values without a calculator?
2. How is the tangent function related to the slope of a line?
3. Why is the tangent of 90 degrees undefined?
4. What is the range and domain of the tangent function?
5. How do trigonometric functions apply to physics problems?

**Tip:** Familiarizing yourself with key trigonometric values and their approximations can be very useful for quick calculations.

Learn how to compute the expression \(\frac{2.1}{\tan(69^\circ)}\) using trigonometric functions. Includes a detailed step-by-step solution and approximate values. Suitable for high school students learning trigonometry.

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