Question

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

Answer 1

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.

Answer 2

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