The Angle From the Area

With the area and two sides known, the rule gives the sine of the angle between them. A sine below 1 belongs to an acute angle and its supplement, and both make a triangle with the same area.

Area 18 with sides 9 and 8: $18 = \frac{1}{2}\cdot 9\cdot 8\cdot \sin\left(\varphi\right)$, so sin φ = 1/2 and φ is 30° or 150°. Both are real triangles: one thin and pointed, one wide open. Nothing here rules either out, so both are answers.