Get an answer in 5 minutes

We'll notify as soon as your question has been answered.

Plus iconAsk a question to our educators
MATHS
Asked by Amar

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?

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.

David's profile picture
Verified
David Mageller
·

6k students helped

Similar Maths questions

Get an answer in 5 minutes

We'll notify as soon as your question has been answered.

Plus iconAsk a question to our educators

Badge showing the text 'New'Learn Maths with Video Lessons

GCSE Maths - Numbers
1hr 28m · 8 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Numbers
Quadratic Inequalities
28m · 3 videos
Iqbal's profile picture
Iqbal Lokman
·

1.3k students helped

Quadratic Inequalities
GCSE Maths - Ratios
1hr 32m · 9 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Ratios
GCSE Maths - Algebra A
56m · 6 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Algebra A

Premium video lessons available now on Scoodle

50% discount available

Scoodle's video lessons make learning easy and fun. Try it for yourself, the first lesson is free!