Answer:
y = 16.5 ft
Step-by-step explanation:
• in the right triangle BCD :
cos(∠BCD) = 8/14
________
• In the right triangle ABC :
cos(∠BCA) = 14/(8+y)
________
Since ∠BCD and ∠BCA are the same one
then
cos(∠BCD) = cos(∠BCA)
Therefore
[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]
[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]
[tex]\Longleftrightarrow 8y+64=196[/tex]
[tex]\Longleftrightarrow 8y=196-64[/tex]
[tex]\Longleftrightarrow 8y=132[/tex]
[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]
[tex]\Longleftrightarrow y=16.5[/tex]
