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

$\text{Area} = \frac{1}{2}ab \sin(C)$

Where:

• $a = 10.87 \, \text{in}$
• $b = 6.17 \, \text{in}$
• $C = 15.21^\circ$

Let's substitute the given values into the formula and calculate the area.

$\text{Area} = \frac{1}{2}(10.87)(6.17) \sin(15.21^\circ)$

I'll calculate that for you now.The area of the triangle ABC is approximately 8.8 square inches.

Would you like further details or clarifications on this solution? Here are some related questions:

1. How can the area of a triangle be calculated if only the three sides are given?
2. What other methods can be used to calculate the area of a triangle besides the formula with two sides and the included angle?
3. How do you convert degrees to radians, and why is that necessary for trigonometric calculations?
4. What is the significance of the sine function in calculating areas of triangles?
5. How do you calculate the perimeter of a triangle given the lengths of its sides?

Tip: When working with angles in trigonometric functions, always ensure they are in the correct unit (degrees or radians) for accurate results.