Part B: Real World Problems The map below shows the flight path for someone traveling from Washington DC and passing above Indianapolis, Indiana; Lincoln, Nebraska $($hometown of the University of Nebraska High School!$)$ and landing in San Francisco. For the sake of clarity, we will assume that the plane is flying due West the entire trip. The plane$$s engines put out enough power to fly at $545$ mph if there is no wind $($but they could put out more if needed$).$ When the plane crosses the border to Utah, it encounters a cross wind of $15$ mph $5$ degrees West of North. What speed and direction must the plane head in to keep going due West at $545$ mph$?$Please show all your work including both a diagram and algebraic solution.