Answer:
Explanation:
To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees.
Given:
b = 31.9
c = 14.7
C = 27.8°
To find angle A, we can use the Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
We know b, c, and C, so we can substitute the values:
a^2 = 31.9^2 + 14.7^2 - 2 * 31.9 * 14.7 * cos(27.8°)
Now, we can solve for a:
a = sqrt(31.9^2 + 14.7^2 - 2 * 31.9 * 14.7 * cos(27.8°))
To find angle B, we can use the Law of Sines:
sin(B)/b = sin(A)/a
We know b and a, so we can substitute the values:
sin(B)/31.9 = sin(A)/a
Now, we can solve for sin(B):
sin(B) = (sin(A)/a) * 31.9
Finally, we can solve for angle B:
B = arcsin((sin(A)/a) * 31.9)
To find angle C, we can subtract angles A and B from 180°:
C = 180° - A - B
Now, we can calculate the values:
A = acos((b^2 + c^2 - a^2) / (2 * b * c))
B = arcsin((sin(A)/a) * 31.9)
C = 180° - A - B
Using the given values, we can calculate the triangle:
A ≈ acos((31.9^2 + 14.7^2 - a^2) / (2 * 31.9 * 14.7))
B ≈ arcsin((sin(A)/a) * 31.9)
C ≈ 180° - A - B
Please note that the final numerical calculation is required to provide the exact values for A, B, and C.