Trig help!!

Well...
Actually it seems quite complicated but I may try to solve.
If it's still in effect - contact me)

8^2=8^2+a^2-2*8*a*cos(62)

64=64+a^2-16a*cos(62) | -64 on both sides
64-64=64-64+a^2-16a*cos(62)
a^2-16a*cos(62) = 0

a^2-16*cos(62)*a = 0
define constant z as "-16*cos(62)"
a^2+z*a = 0
a*a+z*a=0
a* ( a + z ) = 0

this is zero if a or ( a + z ) is zero.
a is zero if a = 0. (solution 1)
a+z=0 is zero if a=16*cos(62)=7.511545004574252 (solution 2)

solution {a=7.511545004574252, a=0}