Final answer:
The area of the triangle with two sides measuring 12 and 24 and an angle of 60 degrees between them is 72√3 square units.
Step-by-step explanation:
To find the area of a triangle, you can use the formula ½ × base × height when you know the lengths of the base and the height. However, in this case, we have two sides and the angle between them given. For such a scenario, we can use the formula ½ × a × b × sin(C) where a and b are the sides of the triangle and C is the angle between them.
Given the sides of 12 and 24 and an angle of 60 degrees between them, the area can be computed as follows:
Area = ½ × 12 × 24 × sin(60°)
Sin(60°) is equal to √3/2.
Therefore, Area = ½ × 12 × 24 × (√3/2)
Area = 6 × 24 × (√3/2)
Area = 144 × (√3/2)
Thus, the area of the triangle is 72√3 square units.