נתונים (∙{\displaystyle \bullet } ) :∠ACB=90∘CD⊥AB∠ACE=∠BCE=902=45∘BC=15cm∠CAB=25∘{\displaystyle {\begin{aligned}&\angle ACB=90^{\circ }\\&CD\perp AB\\&\angle ACE=\angle BCE={\frac {90}{2}}=45^{\circ }\\&BC=15_{cm}\\&\angle CAB=25^{\circ }\\\end{aligned}}}
צ"ל : DE=?{\displaystyle DE=?}
הוכחה :△ABC∠BAC=25∘∙∠ACB=90∘∙↓∠ABC=90∘−25∘=35∘triangleDCB∠CDB=90∘∙↓∠DCB=90∘−65∘=25∘(∗1)∠BCE=45∙↓∠DCE=∠BDE−∠BAC=20∘(∗2)△BCDBC=15∙∠DCB=25∘(∗1)cos∠BCD=DCBCcos25=DC15↓DC=13.595△DECtan∠DCE=DECDtan20=DE13.595DE=4.948◼{\displaystyle {\begin{aligned}&\triangle ABC\\&\angle BAC=25^{\circ }\bullet \\&\angle ACB=90^{\circ }\bullet \\&\downarrow \\&\angle ABC=90^{\circ }-25^{\circ }=35^{\circ }\\&triangleDCB\\&\angle CDB=90^{\circ }\bullet \\&\downarrow \\&\angle DCB=90^{\circ }-65^{\circ }=25^{\circ }(*1)\\&\angle BCE=45\bullet \\&\downarrow \\&\angle DCE=\angle BDE-\angle BAC=20^{\circ }(*2)\\&\triangle BCD\\&BC=15\bullet \\&\angle DCB=25^{\circ }(*1)\\&\cos \angle BCD={\frac {DC}{BC}}\\&\cos 25={\frac {DC}{15}}\\&\downarrow \\&DC=13.595\\&\triangle DEC\\&tan\angle DCE={\frac {DE}{CD}}\\&tan20={\frac {DE}{13.595}}\\&DE=4.948\blacksquare \\\end{aligned}}}