Final answer:
To calculate angle A in the triangle with given sides, the Law of Cosines is used, resulting in angle A being approximately 44.4153086 degrees, which is closest to the 45° answer choice.
Step-by-step explanation:
To calculate angle A in a triangle with sides A = 10 m, B = 12 m, and C = 14 m, we can use the Law of Cosines which gives us an equation to find the cosine of the angle opposite the side of known length. The Law of Cosines formula is given by:
c² = a² + b² - 2*a*b*cos(C),
where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite side c. By rearranging this formula to solve for cos(C), we have:
cos(C) = (a² + b² - c²)/(2*a*b).
Plugging in our values for A, B, and C, we get:
cos(A) = (B² + C² - A²)/(2*B*C)
cos(A) = (12² + 14² - 10²)/(2*12*14)
cos(A) = (144 + 196 - 100)/(336)
cos(A) = 240/336
cos(A) = 0.714285714
Angle A is therefore the inverse cosine of 0.714285714, which is approximately 44.4153086 degrees.
Therefore, the closest answer choice would be B) 45°.