Answer:
a ≈ 6.8, B ≈ 50°, C ≈ 82°
Explanation:
You want to solve the triangle with A=48°, b=7, c=9.
Law of Cosines
The relation given by the law of cosines is ...
a² = b² +c² -2bc·cos(A)
a² = 7² +9² -2·7·9·cos(48°) ≈ 45.6895
a ≈ √45.6895 ≈ 6.76 ≈ 6.8
Law of Sines
The law of sines can be used to find one of the other angles:
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(9/6.7594·sin(48°)) ≈ 81.68° ≈ 82°
The remaining angle can be found from the sum of angles in a triangle:
B = 180° -A -C = 50°
The solution is a ≈ 6.8, B ≈ 50°, C ≈ 82°.