Asked by AmarMaths 💯

I need help on a maths question: A plane flies 300km from an airport, A, on a bearing of 240°.The plane turns and travels for 400km on a bearing of 050°. a) Using a scale of 1 cm to 50km, draw an accurate drawing of the flight path of the plane. b) What is the bearing that the plane must travel on to return to the airport?

David Mageller

If you love what you do, you'll never work a day in your life - Someone

In my answer, I will be assuming the bearing is relative, i.e. we figure out the bearing based on the current direction. I cannot upload a picture so I will be answering part B. Let’s call the starting point A, the second point after 300km B and the third point C. The angle at points A, B and C, will be called a, b and c, respectively. If we draw the diagram, we can see that the point form a triangle ABC, and we know: AB = 300 BC = 400 c = 130 degrees First we can use the Cosine rule to find the length AC. AC^2 = 400^2 + 300^2 + 2*400*300*cos(130) AC^2 = 95730.9736… AC = 309.404 (3dp) Now that we have AC we can use sine rule to find the size of angle c. sin(c) = sin(130) * 300/309.404 c = sin-1(sin(130) * 300/309.404) c = 47.96 degrees (2dp) The bearing from the final direction is a clockwise turn until we are 47.96 degrees from the line BC. So: 180 - 47.96 = 132.04 degrees is the final bearing.

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