The image shows another trigonometric problem involving a right triangle. Let's analyze the given problem:

1. Find the length of the hypotenuse: The triangle has legs of lengths $6$ and $8$. Using the Pythagorean theorem: $c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$

2. Find the tangent of the angle $\theta$ opposite to the leg of length $6$: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{8} = \frac{3}{4}$

Summary

1. The length of the hypotenuse $c$ is $10$.
2. The tangent of the angle $\theta$ is $\frac{3}{4}$.

Would you like more details or have any questions?

Here are five more questions you might be interested in:

1. How do you find the sine and cosine of the angle $\theta$?
2. Can you explain how to solve for angles using inverse trigonometric functions?
3. How do you use the unit circle to find trigonometric values?
4. What are the identities for sum and difference of angles?
5. How can you apply the Law of Sines and the Law of Cosines in non-right triangles?

Tip: Always remember to reduce fractions to their simplest form when dealing with trigonometric ratios for easier interpretation and further calculations.