נתון ( ∙ {\displaystyle \bullet } ): A B = A C = B C ∠ D = 90 ∘ ∠ B A D = ∠ D A C B D = C D = x A E = D E {\displaystyle {\begin{aligned}&AB=AC=BC\\&\angle D=90^{\circ }\\&\angle BAD=\angle DAC\\&BD=CD=x\\&AE=DE\\\end{aligned}}}
צ"ל : ∠ E B D = ? {\displaystyle \angle EBD=?}
הוכחה : A B = A C = B C ∙ ↓ ∠ B A C = ∠ A B C = ∠ B C A = 60 ∘ △ A D C tan D C A = A D D C tan 60 = A D x A D = 1.732 x A E = E D = A D 2 = 1.732 x 2 = 0.866 ↓ △ B E D tan E B D = E D B D tan E B D = 0.866 x x ∠ B E D = 40 / 892 {\displaystyle {\begin{aligned}&AB=AC=BC\bullet \\&\downarrow \\&\angle BAC=\angle ABC=\angle BCA=60^{\circ }\\&\triangle ADC\\&\tan DCA={\frac {AD}{DC}}\\&\tan 60={\frac {AD}{x}}\\&AD=1.732x\\&AE=ED={\frac {AD}{2}}={\frac {1.732x}{2}}=0.866\\&\downarrow \\&\triangle BED\\&\tan EBD={\frac {ED}{BD}}\\&\tan EBD={\frac {0.866x}{x}}\\&\angle BED=40/892\end{aligned}}}
