Question

Lucy has two star systems left to visit on her voyage, but her ship is running low on fuel. The first system, KA-7, is 1200 light years (1.Y.) away while the second system, KA-11, is 1700 1.Y.. Her top priority is to visit star system KA-7. To determine if she'll also be able to visit KA-11, she must find the distance between KA-7 and KA-11. If Lucy sees an angle of 52° between KA-7 and KA-11, how far are KA-7 and KA-11 apart?

Answer 1

1,348 Light Years

Explanation:

In the triangle ABC attached, Lucy's distance to KA-7 is AB while her distance to KA-11 is AC.

We are to determine the distance BC from KA-7 (at point B) to KA-11 (at point C).

Using Law of Cosines

`a^2=b^2+c^2-2bcCos A\\a^2=1700^2+1200^2-2(1700)(1200)Cos 52^\circ\\a^2=4330000-2511898.8193\\a^2=1818101.1807\\a=√(1818101.1807) \\a=1348.37\\a \approx 1348$ L.Y.`

Therefore, KA-7 and KA-11 are approximately 1,348 Light Years apart.