$$d=\sqrt{A^2+B^2+C^2}$$
$$\tan \alpha =\frac{C}{A} \Rightarrow C=A\tan \alpha \ \ , \ \ \tan \beta =\frac{B}{A} \Rightarrow B=A\tan \beta $$
$$d=\sqrt{A^2+A^2\tan^2 \beta +A^2\tan^2\alpha} \\ \Rightarrow d=\sqrt{A^2(1+\tan^2 \alpha +\tan^2 \beta)} \\ \Rightarrow d=A\sqrt{1+\tan^2 \alpha +\tan^2 \beta} \\ \Rightarrow A=\frac{d}{\sqrt{1+\tan^2 \alpha +\tan^2 \beta}}$$