Answer:
To solve the triangle with given side lengths, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles.
1. Let's label the angles opposite the corresponding sides as A, B, and C, and the lengths of the sides as a, b, and c, respectively.
2. Now, we can use the Law of Cosines, which states that c^2 = a^2 + b^2 - 2ab*cos(C), where C is the angle opposite side c.
3. Plugging in the values, we have:
c^2 = 1250^2 + 860^2 - 2 * 1250 * 860 * cos(C)
c^2 = 1562500 + 739600 - 2152000 * cos(C)
c^2 = 2302100 - 2152000 * cos(C)
4. To find the value of cos(C), we can rearrange the equation:
cos(C) = (2302100 - c^2) / (2152000)
5. Now, we can use the inverse cosine function to find the value of angle C:
C = cos^(-1) [(2302100 - c^2) / (2152000)]
6. Finally, to find angles A and B, we can use the Law of Sines. This law states that a / sin(A) = b / sin(B) = c / sin(C).
7. We can rearrange the equation to solve for sin(A) and sin(B):
sin(A) = (a / c) * sin(C)
sin(B) = (b / c) * sin(C)
8. Using the values given, we can calculate sin(A) and sin(B) using the values of a, b, c, and C that we found earlier.
By following these steps, we can determine the values of angles A, B, and C in the triangle with side lengths a = 1250 in, b = 860 in, and c = 747 in.
Explanation: