נתון ( ∙ {\displaystyle \bullet } ): A B = A C ∠ A B D = ∠ 23 ∘ ∠ A D B = 90 ∘ {\displaystyle {\begin{aligned}&AB=AC\\&\angle ABD=\angle 23^{\circ }\\&\angle ADB=90^{\circ }\\\end{aligned}}}
צ"ל : יחס בין שוקי הבסיס C B A C {\displaystyle \ {\frac {CB}{AC}}}
הוכחה : △ D C B ∠ D B C = 23 ∘ ∙ ∠ A D B = 90 ∘ ∙ ↓ ∠ A C B = 90 − 23 = 67 ∘ ∠ C A B = 180 − 67 ∗ 2 = 46 ∘ △ A B D A B = A C = x sin C A B = D B A B sin 46 = D B x D B = 0.719 x △ B D C cos ∠ D B C = D B B C cos 23 = B C 0.719 x B C = 0.719 x 0.92 = 0.718 x ↓ A B B C = x 0.718 x A C B C = 1 0.781 A C B C = 1.279 {\displaystyle {\begin{aligned}&\triangle DCB\\&\angle DBC=23^{\circ }\bullet \\&\angle ADB=90^{\circ }\bullet \\&\downarrow \\&\angle ACB=90-23=67^{\circ }\\&\angle CAB=180-67*2=46^{\circ }\\&\triangle ABD\\&AB=AC=x\\&\sin CAB={\frac {DB}{AB}}\\&\sin 46={\frac {DB}{x}}\\&DB=0.719x\\&\triangle BDC\\&\cos \angle DBC={\frac {DB}{BC}}\\&\cos 23={\frac {BC}{0.719x}}\\&BC={\frac {0.719x}{0.92}}=0.718x\\&\downarrow \\&{\frac {AB}{BC}}={\frac {x}{0.718x}}\\&{\frac {AC}{BC}}={\frac {1}{0.781}}\\&{\frac {AC}{BC}}=1.279\\\end{aligned}}}
