When we know all 3 sides we use tha law of cosines:
cos(A) = (b² + c² -a²) ÷ (2bc)
cos (A) = (64 + 81 -49) / (289)
cos (A) = 96 / 144
cos (A) = 0.6666666667
angle A = 48.19 degrees
(the side opposite this angle is 7)
Next we can use the law of sines
sin ∠B = (b • sin(A)) ÷ a
sin ∠B = (8sin(48.19)) / 7)
sin ∠B = (8 0.74536)/7
sin ∠B =
0.85184
Angle B = 58.412 Degrees
Angle C = 180 -48.19 -58.412
Angle C = 73.398
All angles are acute and so it is an acute triangle.
