In trigonometry, the tangent (often abbreviated as "tan") of an angle in a right triangle is a ratio that relates the lengths of two specific sides of the triangle.

For a given angle \(\theta\) in a right triangle:
- The **opposite side** is the side opposite to the angle \(\theta\).
- The **adjacent side** is the side next to the angle \(\theta\) (not the hypotenuse).

The tangent of the angle \(\theta\) is defined as the ratio of the length of the opposite side to the length of the adjacent side:

\[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \]

Here's a simple example:

1. Imagine a right triangle where:
   - The length of the side opposite to the angle \(\theta\) is 3 units.
   - The length of the side adjacent to the angle \(\theta\) is 4 units.

2. The tangent of the angle \(\theta\) is then:

\[ \tan \theta = \frac{3}{4} = 0.75 \]

So, \(\tan \theta\) gives you a way to compare how steep the angle \(\theta\) is by comparing the lengths of these two sides.

In your problem, \(\tan \theta = \frac{9.3}{4.8}\). This ratio tells you the relationship between the lengths of the opposite side (9.3 m) and the adjacent side (4.8 m) for the angle \(\theta\).

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. What are the other trigonometric ratios besides tangent?
2. How do you calculate sine and cosine in a right triangle?
3. What is an inverse trigonometric function?
4. How can I use trigonometric ratios to find missing sides of a triangle?
5. What are some practical applications of tangent in real life?

**Tip:** Remember that trigonometric functions are based on right triangles, and they help you understand the relationships between the angles and sides of these triangles.

Explore the definition and examples of tangent in trigonometry. Learn how to calculate tangent in a right triangle using the ratio of the opposite side to the adjacent side. Includes a detailed explanation and a practical example calculation. Suitable for students in Grades 9-12.

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