see the picture attached to better understand the problem
we know that
in the right triangle ABC
tan 64°=AB/AC------> AB=AC*tan 64°-----> AB=x*tan 64°---> equation 1
in the right triangle ABD
tan 43°=AB/DA----> AB=DA*tan 43°---> AB=(240+x)*tan 43°---> equation 2
equate equation 1 and equation 2
x*tan 64°-=(240+x)*tan 43°---->x*tan 64=240*tan 43+x*tan 43
x*[tan 64-tan 43]=240*tan 43-----> x=240*tan 43/[tan 64-tan 43]
x=200.22 ft
AB=x*tan 64----> AB=200.22*tan 64-----> AB=410.51 ft
the answer is
410.51 ft
