Lighthouse A is 25 northeast of observation station C, Lighthouse B is 35 southeast of observation station C, and ACB =180-25-35 =120.

According to cosine theorem

c？ =a？ +b？ -2ab cosC=a？ +a？ +a？ =3a？

(cosC= 120 =-0.5)

C= root number 3 a

That is to say, the distance between lighthouse A and lighthouse B is the root number 3 a(km).