Final answer:
The correct answer is option a. The area of an obtuse triangle with sides 23.1 mm and 15.0 mm forming an angle of 123° is found using the formula involving sine of the angle. The calculation results in an area of approximately 145.3 mm², which corresponds to answer option (a).
Step-by-step explanation:
The question concerns the calculation of the area of a triangle with given side lengths and an angle. In an obtuse triangle, one angle is greater than 90°, and the sum of all angles is 180°. The area of a triangle can be calculated using the formula:
Area = ½ × base × height
However, in this case, we have two sides and the included obtuse angle of 123° but no height. We need to use another approach to find the area. The formula for the area of a triangle when two sides and the included angle are known is given by:
Area = ½ × side1 × side2 × sin(angle)
For our triangle with sides of 23.1 mm and 15.0 mm forming an angle of 123°, the area can be calculated as follows:
Area = ½ × 23.1 mm × 15.0 mm × sin(123°)
Using a calculator:
Area = ½ × 23.1 × 15.0 × sin(123°)
Area = 0.5 × 23.1 × 15.0 × 0.8387...
Area = ½ × 23.1 × 15.0 × 0.8387...
Area = 145.36515... mm²
Rounding to the nearest tenth gives us an area of 145.3 mm², which is answer option (a).