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The problem provided in the image asks to solve the given triangle by finding the angles, given the sides, and the side lengths are given in centimeters.

The triangle sides are:
- \( a = 7 \) cm
- \( b = 10 \) cm
- \( c = 12 \) cm

This is a standard problem of solving a triangle using the Law of Cosines to find the angles. Let's calculate the angles \( A \), \( B \), and \( C \) of the triangle.

### Step 1: Use the Law of Cosines
The Law of Cosines states:
\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}
\]
\[
\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}
\]
\[
\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}
\]

### Step 2: Calculate Angle \( A \)
\[
\cos(A) = \frac{10^2 + 12^2 - 7^2}{2 \times 10 \times 12} 
\]
\[
\cos(A) = \frac{100 + 144 - 49}{240}
\]
\[
\cos(A) = \frac{195}{240} \approx 0.8125
\]
\[
A \approx \cos^{-1}(0.8125) \approx 35.3^\circ
\]

### Step 3: Calculate Angle \( B \)
\[
\cos(B) = \frac{7^2 + 12^2 - 10^2}{2 \times 7 \times 12} 
\]
\[
\cos(B) = \frac{49 + 144 - 100}{168}
\]
\[
\cos(B) = \frac{93}{168} \approx 0.5536
\]
\[
B \approx \cos^{-1}(0.5536) \approx 56.4^\circ
\]

### Step 4: Calculate Angle \( C \)
Since the sum of all angles in a triangle is \( 180^\circ \), we can find \( C \) by:
\[
C = 180^\circ - A - B 
\]
\[
C = 180^\circ - 35.3^\circ - 56.4^\circ \approx 88.3^\circ
\]

### Summary of Results:
- Angle \( A \approx 35.3^\circ \)
- Angle \( B \approx 56.4^\circ \)
- Angle \( C \approx 88.3^\circ \)

Would you like further details on any of these steps or have any questions?

### Relative Questions:
1. How can the Law of Cosines be derived geometrically?
2. What is the significance of the Law of Cosines in solving non-right triangles?
3. How would the calculations differ if this were a right triangle?
4. What other methods can be used to solve a triangle given different sets of information (e.g., SAS, SSA, etc.)?
5. How do you convert between degrees and radians for angle measures?

### Tip:
Always cross-check the sum of the calculated angles in a triangle to ensure they add up to \(180^\circ\). This helps verify the accuracy of your calculations.

Resolve el siguiente triángulo oblicuángulo, encontrando los valores de los ángulos, considere las medidas en cm.

Learn how to solve a non-right triangle by finding the angles using the Law of Cosines. This example uses given side lengths a = 7 cm, b = 10 cm, and c = 12 cm to find angles A, B, and C. Suitable for high school trigonometry students.

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