Are the triangle side lengths 7,8,9 acute, right, or obtuse?

Acute ... 8^2 + 7^2 = 113 and 9^2 is 81 so ... 113=81 since c^2 is less than a ^2 + b^2

When we know all 3 sides we use tha law of cosines:

cos (A) = (b² + c² - a²) : (2bc)

cos (A) = (64 + 81 - 49) / (2*8*9)

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 = (8*sin (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.