Given:
[tex]\begin{gathered} AD=BD=8.9m \\ DC=15.5m \\ \angle C=27.5\degree \end{gathered}[/tex]
Required:
To find the length of chord AB.
Explanation:
Now consider the figure.
From the sine rule,
[tex]\begin{gathered} \frac{\sin C}{BD}=\frac{\sin B}{DC} \\ \\ \frac{\sin27.5}{8.9}=\frac{\sin B}{15.5} \\ \\ \sin B=\frac{\sin27.5}{8.9}\times15.5 \\ \\ B=126.46\degree \end{gathered}[/tex]
Now
[tex]\begin{gathered} \angle A=180-126.46 \\ =53.54\degree \end{gathered}[/tex][tex]\begin{gathered} \angle D=180-53.54-53.54 \\ =72.92\degree \end{gathered}[/tex]
Now from the sine rule
[tex]\begin{gathered} \frac{\sin D}{AB}=\frac{\sin B}{AD} \\ \\ \frac{\sin72.92}{AB}=\frac{\sin53.54}{8.9} \\ \\ AB=\frac{\sin72.29}{\sin53.54}\times8.9 \\ \\ AB=10.54m \end{gathered}[/tex]
Final Answer:
The length of chord AB is 10.54m.
