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let projectile is projected at a distance a from the corner of the base so its range must be
R = a+10√3 + a
= 2a +10√3
so 2a + 10√3 = V2 sin2b/2g
or g/v2cos2b = sinb/(2a+10√3) ....................1
select first two corner point of hexagon ,if the projectile pass through these point then by symmetry it will also pass through oteher two ppoints
points are ( a-10√3cos60 , 10√3sin60) and (a,20√3sin60)
use the general equation
y =x tanb - gx2/2v2cos2b
put above these two point and put the value of g/v2cos2b = sinb/(2a+10√3)
then u will get 2 equation in a and tanb
solve it and then easly u can get desired result
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