height n distance

 

 

As is clear from the side and top views, the length of the field is x.

Now

tan α = h/a

h = a tan α

tan β = h/(a+x)

a + x = h/tan β = a tan α/tan β

Length of the field, x =   (a tan α/tan β) - a = a(tan α - tan β)/tan β

Regards,

Team,

TopperLearning.