Help with a bearing problem?

[Knightwing]

A plane takes off from an airport and flies in the heading of E 70° N for 18 miles. At that time, a course correction is made, and the plane flies a further 40 miles in the heading E 25° N. Calculate the distance between the plane and the airport, and the bearing from the airport to the plane.

 

[lev888]

A plane takes off from an airport and flies in the heading of E 70° N for 18 miles. At that time, a course correction is made, and the plane flies a further 40 miles in the heading E 25° N. Calculate the distance between the plane and the airport, and the bearing from the airport to the plane.

Please read posting guidelines.
Start with a diagram.

 

[Otis]

Hi Knightwing. Is your class working with the right-triangle definitions for sine, cosine, tangent? Are you learning about vectors?

Do you understand how to sketch the given bearings? Where did you get stuck?

?

 

[HallsofIvy]

One leg is at "70 degrees N of E" which, on a 360 degree compass, is 90- 70= 20 degrees. The next leg is at "25 degrees N of E" which, on a 360 degree compass, is 90- 25= 65 degrees. The angle between the two legs is 180+ 20- 65=135 degrees. You have a triangle with two legs of length 18 and 40 miles and angle between them 135 degrees. Use the cosine law.