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The largest angle in an obtuse triangle measures 123°. The sides that form the angle measure 23.1 millimeters and 15.0 millimeters. What is the area of the triangle?

a. 145.3mm²
b. 173.3mm²
c. not enough information to solve
d. 290.6mm²

1 Answer

4 votes

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).

User Marek Rycharski
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