To find the area of a triangle given two sides and the included angle, we can use the formula:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

Where:

• $a = 10 \, \text{cm}$
• $b = 13 \, \text{cm}$
• $C = 105^\circ$

Let's calculate the area.

I'll compute this now.The area of the triangle is $62.8 \, \text{cm}^2$, rounded to one decimal place.

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions to deepen understanding:

1. How does the sine rule apply to triangles with different angles?
2. Can this formula be used for all triangles, and why?
3. How can you calculate the area if the angle is unknown but all sides are given?
4. What would change if one of the angles was a right angle?
5. How would the formula differ for non-Euclidean triangles?

Tip: The sine function in triangle area calculations is always used with the angle between the two sides.