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On a illustré une pièce de métal servant à la fabrication d'un hélicoptère.
Sachant que l'aire de cette pièce est de 20,3 dm?, déterminez la mesure de l'angle
С.

We are given a triangle with the following dimensions:

- Side \( AB = 5.94 \, \text{dm} \)
- Side \( BC = 8.18 \, \text{dm} \)
- The area of the triangle \( \text{Area} = 20.3 \, \text{dm}^2 \)

We are tasked with finding the measure of angle \( C \) in the triangle.

The area of a triangle can be found using the formula:

\[
\text{Area} = \frac{1}{2} \times AB \times BC \times \sin(C)
\]

Substituting the known values:

\[
20.3 = \frac{1}{2} \times 5.94 \times 8.18 \times \sin(C)
\]

Let's solve for \( \sin(C) \), and then use it to determine angle \( C \).The measure of angle \( C \) is approximately \( 56.68^\circ \).

Would you like more details or further explanations?

Here are 5 related questions for deeper understanding:
1. How can the sine rule be used to find other angles in the triangle?
2. What other methods could be used to find angle \( C \)?
3. Can you calculate the remaining angles \( A \) and \( B \) using trigonometry?
4. What are some real-world applications of triangle area calculations?
5. How does this formula for area relate to other area formulas like Heron's formula?

**Tip:** Remember that the sine function in trigonometry is key to solving many problems involving angles in non-right triangles, especially when working with known areas.

On a illustré une pièce de métal servant à la fabrication d'un hélicoptère. Sachant que l'aire de cette pièce est de 20,3 dm², déterminez la mesure de l'angle C.

Learn how to calculate the angle C in a triangle with sides AB = 5.94 dm, BC = 8.18 dm, and an area of 20.3 dm². This problem uses trigonometric principles and the formula for the area of a triangle to find the unknown angle.

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