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Dengta mathematics
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).