Measuring From Eye Level

An angle of elevation is measured at the eye, not at the feet. Your eye is about 1.5 m above the ground, so the right triangle sits on a level line through your eye, and the triangle's height is only the part of the building above that line.

From 12 m away, with your eye 1.5 m up, the top of a wall is at 40°. The part above your eye is $h-1.5$, so $\tan\left(40^{\circ}\right) = \frac{h-1.5}{12}$. Multiply by 12 and add 1.5: $h = 12\tan\left(40^{\circ}\right)+1.5$, about 11.57 m. Forgetting the eye height would give 10.07 m, short by exactly 1.5.