There are 3 airports, A , E and G. G is 200km from A.E is 160 km from A From G the bearing of A is 052 degrees. From A the bearing of E is 216 degrees. What's the distance between A and G?

360- 216 = 144
144-52 = 128
144-128 = 16

a^2 = b^2+c^2-(2*b*c)*cos(A)
a^2 = 160^2 + 200^2 - ( 2 * 160 * 200) * (cos 16)
a^2 = 4079.25...
a = 63.9 km <--- ?

Looks good to me.

Thank you

To find the distance between airports A and G, we can use the Law of Cosines. The formula is:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we want to find the distance between A and G, which means c is the distance between A and G.

Given:
- Distance between A and E (b): 160 km
- Distance between A and G (c): unknown
- Angle at G (C): 052 degrees
- Angle at A (B): 216 degrees

We need to find the angle at E (A) in order to use the Law of Cosines.
Angle A + Angle B + Angle C = 180 degrees, so:
216 + 052 + Angle A = 180
Angle A = 180 - 216 - 052
Angle A = -88 degrees

Since angles cannot be negative, we need to convert -88 degrees to its positive equivalent:
Angle A = -88 + 360
Angle A = 272 degrees

Now we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 160^2 + 200^2 - 2 * 160 * 200 * cos(270)
c^2 = 4079.25
c ≈ 63.9 km

So, the distance between airports A and G is approximately 63.9 km.