Answer:
The exact length of [tex]BD[/tex] would be [tex]6.70[/tex]
Step-by-step explanation:
Given [tex]BC=10\ and\ AB=6[/tex]
Also, ∠[tex]DBC=x[/tex] and ∠[tex]ABD=x[/tex]
So, ∠[tex]ABC=[/tex]∠[tex]DBC+[/tex]∠[tex]ABD=x+x=2x[/tex]
Now, in Δ[tex]ABC[/tex]
[tex]cos(2x)=\frac{AB}{BC}\\\\cos(2x)=\frac{6}{10}\\\\cos(2x)=0.6\\\\taking\ cos^{-1}\ both\ side\ we\ get, \\\\2x=cos^{-1}(0.6)\\\\2x=53.13\\\\x=\frac{53.13}{2}=26.56[/tex]
Now, in Δ[tex]ABD[/tex]
[tex]cos(26.56)=\frac{AB}{BD}\\\\cos(26.56)=\frac{6}{BD}\\\\0.895=\frac{6}{BD}\\\\BD=\frac{6}{0.895}\\\\BD=6.70[/tex]
So, the exact length of [tex]BD[/tex] would be [tex]6.70[/tex]
