Answer:
To solve the triangle with the given parts A = 98.7, b = 5, and c = 15, we can use the Law of Cosines and Law of Sines.
Explanation:
1. First, let's find angle C using the Law of Cosines:
- c^2 = a^2 + b^2 - 2ab * cos(C) (where a is the side opposite to angle C)
- Substituting the known values: 15^2 = a^2 + 5^2 - 2 * a * 5 * cos(C)
- Simplifying: 225 = a^2 + 25 - 10a * cos(C)
- We don't have enough information to solve for angle C using the given parts, so we can't determine the exact value of angle C.
2. However, we can use the Law of Sines to find the remaining angles:
- sin(A) / a = sin(C) / c (where a and c are the opposite sides of angles A and C, respectively)
- Substituting the known values: sin(98.7) / a = sin(C) / 15
- We don't have enough information to solve for angle C using the given parts, so we can't determine the exact value of angle C.
3. Given that we can't determine the exact values of angles A and C, we can find angle B using the fact that the sum of all angles in a triangle is 180 degrees:
- Angle B = 180 - A - C
- Angle B = 180 - 98.7 - C
- Angle B = 81.3 - C
In summary, we can't determine the exact values of angles A, B, and C without additional information. We know that angle B is equal to 81.3 - C, but without knowing the value of angle C, we can't find the exact value of angle B.