Q:

Given: ΔАВС, m∠ACB = 90° CD ⊥ AB, m∠ACD = 60° BC = 6 cm. Find: АD

Accepted Solution

A:
Answer:[tex]AD=9\ cm[/tex]Step-by-step explanation:Step 1In the right triangle BCDFind  the measure of CDwe know thatm∠DCB = [tex]90\°-60\°=30\°[/tex][tex]cos(30\°)=\frac{CD}{BC}[/tex][tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]so[tex]\frac{CD}{BC}=\frac{\sqrt{3}}{2}[/tex]solve for CD[tex]CD=BC\frac{\sqrt{3}}{2}[/tex]we have[tex]BC=6\ cm[/tex]substitute[tex]CD=(6)\frac{\sqrt{3}}{2}[/tex][tex]CD=3\sqrt{3}\ cm[/tex]Step 2In the right triangle ACDFind  the measure of ADwe know that[tex]tan(60\°)=\frac{AD}{CD}[/tex][tex]tan(60\°)=\sqrt{3}[/tex]so[tex]\frac{AD}{CD}=\sqrt{3}[/tex]solve for AD[tex]AD=(CD)\sqrt{3}[/tex]we have[tex]CD=3\sqrt{3}\ cm[/tex]substitute[tex]AD=(3\sqrt{3})\sqrt{3}=9\ cm[/tex][tex]AD=9\ cm[/tex]