Tangent lines and angles?

Question

The tangent line to the graph of f(x)=x^2+5x-24 at x=8 meets the x-axis at an angle AOB whose tangent is _____. The angle AOB measures ____ radians.

Answer 1

f(x) = x^2 + 5x - 24
f'(x) = 2x + 5
at x = 8, f'(8) = 16 + 5 = 21
Therefore, the angle with x-axis has a tangent of 21 and the angle is arc tan(21) = 1.5232 radians.

Answer 2

m= 2x+5 = 21 = tangent AOB
(I think that you refer to the angle between the tangent and the positive X axis)
Arctan 21 =1.5232 rad.