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To find the area of triangle \( \Delta VWX \), we can apply the **formula for the area of a triangle using two sides and the included angle**. The formula is:

\[
\text{Area} = \frac{1}{2}ab \sin C
\]

Where:
- \( a \) and \( b \) are the lengths of two sides, and
- \( C \) is the angle between those sides.

In this triangle:
- \( WV \), \( VX \), and \( WX \) are the sides,
- Angle \( W = 66^\circ \),
- Angle \( X = 64^\circ \),
- The side \( VX = 40 \, \text{cm} \).

To solve this:
1. We first need to find the length of the other sides using the **Law of Sines**:
\[
\frac{WV}{\sin X} = \frac{WX}{\sin V} = \frac{VX}{\sin W}
\]
Where \( \sin V = \sin(180^\circ - (66^\circ + 64^\circ)) = \sin 50^\circ \).

Let me calculate the sides using this and then find the area.The lengths of the sides of triangle \( \Delta VWX \) are approximately:
- \( WV \approx 33.5 \, \text{cm} \)
- \( WX \approx 39.4 \, \text{cm} \)

Using these, the area of the triangle is approximately:

\[
\text{Area} \approx 612.8 \, \text{cm}^2
\]

Would you like further explanation or details on this calculation?

Here are 5 related questions:
1. How is the Law of Sines applied in non-right triangles?
2. What other methods can be used to find the area of a triangle?
3. How can we find the perimeter of this triangle using the sides calculated?
4. What is the significance of using radians when computing trigonometric functions in calculations?
5. Can this method be applied to any triangle, or are there exceptions?

**Tip**: When using trigonometric functions in calculations, always ensure you're using the correct angle units (degrees or radians) depending on your calculator or tool.

Find the area of triangle VWX, where the angles at W and X are 66° and 64° respectively, and side VX is 40 cm.

Learn how to find the area of triangle VWX using trigonometry. The problem uses the Law of Sines to find missing sides and applies the area formula for triangles. Given angle W = 66°, angle X = 64°, and side VX = 40 cm, this solution provides step-by-step guidance. Suitable for Grades 9-12.

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