To answer this question, we can use the Cosine Law. We have that the general formula for it is as follows:

We need to remember that angle C is the angle in front of the side c. Then we have - from the graph:
• c = 250mi
,
• a = 230mi
,
• b = 315mi
And we will find the angle Θ as follows - without using units:

Then, if we solve the equation for cosΘ, we will have:


Then, we have:


If we need to find the angle, Θ, we need to apply the inverse function of cosine, arccosine, to both sides of the equation to find it. Then, we have:

Then

If we round the value to the nearest tenth, then we have that:

In summary, therefore, the angle Θ between their flights paths is Θ = 51.8º - rounded to the nearest tenth.