Answer:
c = 29, A = 48°, B = 54°
Step-by-step explanation:
The unknown side is c. Using the last Law of Cosines formula, we find it to be ...
c² = a² +b² -2ab·cos(C)
c² = 22² +24² -2(22)(24)cos(78°) ≈ 840.445
c ≈ √840.445 ≈ 29 . . . . . rounded to integer
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The angle at B can be found using the Law of Sines. We want the angle in the numerator, so we can write the equation as ...
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ arcsin(24/28.9904×sin(78°))
B ≈ 54°
The remaining angle can be found using the sum of angles of a triangle:
A +B +C = 180°
A = 180° -B -C = 180° -54° -78° = 48°
The solution to the triangle is ...
c = 29, A = 48°, B = 54°
