Final answer:
To find the area of triangle ABC, use the formula A = 1/2 * AB * BC * sin(B) with AB = 6, BC = 10, and m∠B = 120°. Sine of 120 degrees is √3/2. After calculations, the area is 15√3 square units. The correct option is A.
Step-by-step explanation:
The problem requires us to find the area of triangle ABC given the length of two sides and the measure of angle B. The formula to use involves the sine function: A = 1/2 * AB * BC * sin(B). We have AB = 6, BC = 10, and m∠B=120°.
To find the sine of 120 degrees, we can use the property that sine function of an angle greater than 90 degrees is the same as the sine of its supplement. So, sin(120°) = sin(180° - 120°) = sin(60°). We know that sin(60°) = √3/2.
Plugging in the values into the area formula:
- A = 1/2 * 6 * 10 * √3/2
- A = 1/2 * 60 * √3/2
- A = 30 * √3/2
- A = 15√3 square units
This corresponds to option A: 15√3 square units.