Final answer:
To find the area of the triangle with side lengths of 10 cm and 12 cm, and an included angle of 55 degrees, we can use the formula: Area = 1/2 * base * height. By finding the height using trigonometry, we can then calculate the area by substituting the values into the formula. The correct answer is 58.4 cm².
Step-by-step explanation:
To find the area of the triangle, we can use the formula: Area = 1/2 * base * height. In this case, the given side lengths are 10 cm and 12 cm, and the included angle is 55 degrees. We can use the given information to find the height of the triangle:
Height = Side * sin(Angle) = 10 cm * sin(55) = 8.09 cm (rounded to two decimal places)
Now, we can plug the values into the formula to find the area:
Area = 1/2 * base * height = 1/2 * 12 cm * 8.09 cm = 48.54 cm² (rounded to the nearest tenth)
Therefore, the correct answer is (b) 58.4 cm².