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.