Answer:
Explanation:
Given:
b = 18.8
c = 26.5
B = 27.9°
To find angle A, we can use the Law of Sines:
sin(A)/a = sin(B)/b
We know B and b, so we can substitute the values:
sin(A)/a = sin(27.9°)/18.8
Now, we can solve for sin(A):
sin(A) = (sin(27.9°)/18.8) * a
To find the value of a, we can use the Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(B)
Substituting the given values:
a^2 = 18.8^2 + 26.5^2 - 2 * 18.8 * 26.5 * cos(27.9°)
Now, we can solve for a:
a = sqrt(18.8^2 + 26.5^2 - 2 * 18.8 * 26.5 * cos(27.9°))
Using the Law of Sines again, we can find angle C:
sin(C)/c = sin(B)/b
Substituting the known values:
sin(C)/26.5 = sin(27.9°)/18.8
Now, we can solve for sin(C):
sin(C) = (sin(27.9°)/18.8) * 26.5
Finally, we can solve for angle C:
C = arcsin((sin(27.9°)/18.8) * 26.5)
To find the smaller value for angle A, we can subtract angle B and angle C from 180°:
A = 180° - B - C
Now, we can calculate the values:
A ≈ 180° - 27.9° - arcsin((sin(27.9°)/18.8) * 26.5)
C ≈ arcsin((sin(27.9°)/18.8) * 26.5)
a ≈ sqrt(18.8^2 + 26.5^2 - 2 * 18.8 * 26.5 * cos(27.9°))
Please note that the final numerical calculation is required to provide the exact values for A, C, and a.