נתונים ( ∙ {\displaystyle \bullet } ) :
AE תיכון. C D ⊥ A B A C ⊥ C B B C = 6 c m C D = 5 c m ↓ ∠ C D B = ∠ A D E = ∠ A C B = 90 ∘ C E = B F = 3 c m {\displaystyle {\begin{aligned}&CD\perp AB\\&AC\perp CB\\&BC=6_{cm}\\&CD=5_{cm}\\&\downarrow \\&\angle CDB=\angle ADE=\angle ACB=90^{\circ }\\&CE=BF=3_{cm}\\\end{aligned}}}
צ"ל : ∠ E O C = ? {\displaystyle \angle EOC=?} הוכחה : △ C D B C D = 5 c m ∙ B C = 6 c m ∙ sin ∠ C B D = D C B D = 5 6 C B D = 56.443 ↓ △ A B C ∠ B A C = 90 − 56.443 = 33.557 ∘ ◼ ↓ tan ∠ A B C = A C B C tan ∠ 56.443 = A C 6 A C = 9.045 c m △ A C E tan ∠ E A C = 3 9.04 ∠ E A C = 18.359 ↓ ∠ B A E = ∠ B A C − E A C = 33.557 − 18.359 = 15.198 ∠ A D O = 90 ∘ ∙ ∠ A O D = 90 − 15.198 = 74.802 ∠ A O D = C O E = 15.198 ◼ ( V e r t i c a l a n g l e s ) {\displaystyle {\begin{aligned}&\triangle CDB\\&CD=5_{cm}\bullet \\&BC=6_{cm}\bullet \\&\sin \angle CBD={\frac {DC}{BD}}={\frac {5}{6}}\\&CBD=56.443\\&\downarrow \\&\triangle ABC\\&\angle BAC=90-56.443=33.557^{\circ }\blacksquare \\&\downarrow \\&\tan \angle ABC={\frac {AC}{BC}}\\&\tan \angle 56.443={\frac {AC}{6}}\\&AC=9.045_{cm}\\&\triangle ACE\\&\tan \angle EAC={\frac {3}{9.04}}\\&\angle EAC=18.359\\&\downarrow \\&\angle BAE=\angle BAC-EAC=33.557-18.359=15.198\\&\angle ADO=90^{\circ }\bullet \\&\angle AOD=90-15.198=74.802\\&\angle AOD=COE=15.198\blacksquare (Verticalangles)\\\end{aligned}}}
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