A Leg Below the Bar

A tangent can put the unknown on the bottom too, when the side you want is the adjacent leg. A building 12 m tall is seen at 40° from a point on the ground. How far is that point from the building?

The height is opposite 40° and the distance d is adjacent: $\tan\left(40^{\circ}\right) = \frac{12}{d}$. Move d across and divide by tan 40°: $d = \frac{12}{\tan\left(40^{\circ}\right)}$, about 14.30 m. The tangent of 40° is below 1, so the distance comes out longer than the height, which fits an angle under 45°.