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To solve the triangle, we need to find the angles based on the given side lengths:

- Side \( a = 5 \, \text{m} \)
- Side \( b = 5 \, \text{m} \)
- Side \( c = 7.5 \, \text{m} \)

We can apply the **Law of Cosines** to find one of the angles first:

\[
\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}
\]

### Let's solve for angle \( C \):
\[
\cos(C) = \frac{5^2 + 5^2 - 7.5^2}{2 \times 5 \times 5}
\]

I'll calculate this next.The angle \( C \) opposite the side \( c = 7.5 \, \text{m} \) is approximately \( 97.18^\circ \).

Next, we can find the other two angles using the Law of Cosines or the Law of Sines. Since the triangle is scalene and the sum of angles in any triangle is \( 180^\circ \), we can use the **Law of Sines** to find one of the remaining angles.

Using the Law of Sines:

\[
\frac{\sin A}{a} = \frac{\sin C}{c}
\]

Let's calculate angle \( A \).It seems like I can't do more advanced data analysis right now. Please try again later.

Would you like me to explain how you can use the Law of Sines yourself to find the remaining angles? Here are some relative questions you might be interested in:

1. How does the Law of Cosines work for different triangles?
2. Can the Law of Sines be used for any type of triangle?
3. What is the difference between scalene and isosceles triangles in terms of angles?
4. How do you verify the sum of angles in a triangle?
5. What is the importance of the triangle inequality theorem?

**Tip**: Always ensure the sum of the angles in a triangle is exactly \(180^\circ\) to check if your calculations are correct!

Find the angles in a triangle with sides 5 m, 5 m, and 7.5 m.

Discover how to find the angles of a triangle with side lengths 5 m, 5 m, and 7.5 m using trigonometric concepts such as the Law of Cosines and the Law of Sines. This problem is suitable for students in Grades 10-12, covering key geometry and trigonometry concepts.

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