Answer :
The solution is:
a = 38.2
b ≈ 22.5
c = 30.0
A = 90°
B = 35°18'
C ≈ 54°42
'
We are given that B = 35°18', a=38.2 and b=32.6. To solve the triangle ABC, we can use the Law of Sines and Law of Cosines.
First, we can find the measure of angle C:
C = 180° - A - B
C = 180° - 90° - 35°18'
C = 54°42'
Next, we can use the Law of Sines to find the length of side c:
sin(A) sin(C)
----- = -----
a c
sin(90°) sin(54°42')
------- = -------
38.2 c
c = 38.2*sin(54°42') / sin(90°)
c = 30.0 (rounded to one decimal place)
Finally, we can use the Law of Cosines to find the length of side b:
b^2 = a^2 + c^2 - 2*a*c*cos(B)
b^2 = 38.2^2 + 30.0^2 - 2*38.2*30.0*cos(35°18')
b ≈ 22.5
Therefore, the solution is:
a = 38.2
b ≈ 22.5
c = 30.0
A = 90°
B = 35°18'
C ≈ 54°42'
Note that since the value of b is less than the value of a, this triangle is an obtuse-angled triangle.
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