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The image contains a problem written in a different language. It appears to be in Serbian, and the problem involves a triangle \(ABC\) where some angles are given. Here’s a translation and interpretation of the problem:

**Translation:**
1. In triangle \(ABC\), it is given that \(\angle ABC = 80^\circ\) and \(\angle BCA = 40^\circ\).
2. a) Find \(\angle CAB\).
   b) Prove that the triangle \(ABC\) is the one that has the maximum area among all triangles with the same base and height.

**Solution:**

### Part a: Finding \(\angle CAB\)
In any triangle, the sum of the interior angles is always \(180^\circ\). Given:
\[
\angle ABC = 80^\circ
\]
\[
\angle BCA = 40^\circ
\]
We can find \(\angle CAB\) as:
\[
\angle CAB = 180^\circ - \angle ABC - \angle BCA = 180^\circ - 80^\circ - 40^\circ = 60^\circ
\]

### Part b: Proving that Triangle \(ABC\) has Maximum Area
To prove that triangle \(ABC\) has the maximum area among all triangles with the same base and height, we can use the property that for a fixed base and height, the triangle with the largest area is the one that forms a right angle between the base and the height.

However, a more rigorous proof would involve showing that in a given set of triangles with a constant base and height, the one with a right angle between these two lines achieves the maximum area. In this triangle, if \(\angle ACB = 90^\circ\), then the area is maximized because the sine of \(90^\circ\) is 1, giving the maximum possible area formula \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\).

Would you like a more detailed explanation or have any questions about this problem? Here are some related questions you might find useful:

1. What is the sine rule, and how can it be applied in triangle problems?
2. How can you use the cosine rule to find an unknown side in a triangle?
3. What is the relationship between angles and side lengths in any triangle?
4. How can we determine if a triangle is obtuse, acute, or right-angled?
5. What is the significance of the area formula for triangles?

**Tip:** When solving geometry problems, always remember that the sum of the angles in any triangle is \(180^\circ\).

In triangle ABC, it is given that ∠ABC = 80° and ∠BCA = 40°. Find ∠CAB and prove that the triangle ABC has the maximum area among all triangles with the same base and height.

This problem involves finding an unknown angle in triangle ABC given two angles, and proving that the triangle has the maximum area among all triangles with the same base and height. Ideal for students in Grades 8-10.

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