Aprēķini divplakņu kakta leņķa pie pamata lielumu grādos.

Let $$S_{base}$$ be the area of the base and $$S_{side}$$ be the area of the side surface. Let $$a$$ be the side of the base. Then $$S_{base} = a^2 = 22\sqrt{3}$$. Thus, $$a = \sqrt{22\sqrt{3}}$$. Let $$h_a$$ be the apothem. Then $$S_{side} = 4 * (1/2 * a * h_a) = 2 * a * h_a = 44$$. Thus, $$a * h_a = 22$$, and $$h_a = 22/a = 22/\sqrt{22\sqrt{3}} = \sqrt{22/\sqrt{3}}$$. The angle $$\alpha$$ satisfies $$\tan(\alpha) = (2h_a)/a = 2h_a/a = 2 * \sqrt{22/\sqrt{3}} / \sqrt{22\sqrt{3}} = 2/(\sqrt[4]{3})^2 = 2/\sqrt{3}$$. Thus, $$\alpha = \arctan(2/\sqrt{3}) \approx 49.1^\circ$$. The angle is approximately 49 degrees.