Bearing problems & Airplane problems

Question

A man travels 6 miles due east, and then 4 miles northwest. What is the direction and distance back to his starting point? 

 

- I want to understand how to set this up using a picture & then solving. Thanks

Answer 1

Hi Alondra,

 

I'll try and get you started. See this graph for a picture of triangle ABC: 

 

https://www.desmos.com/calculator/3xvoqw0ovq

 

After heading from point A 6 miles east, going northwest means North then 45 degrees towards the west. That is represented by angle C on the graph. If you want to see how I was able to draw side CB, open the folder Draw Triangle. That is not pertinent to this problem, however. Side CB has a length of 4. 

 

Use the Law of Cosines to find side c. After you have side c use the Law of Sines to find angle A (in the triangle). Bearing from one point to another is always from north of the starting point clockwise to the destination point. That is why a dropped a perpendicular through point B. Once you have angle A you can find angle B₁. This will help you find the bearing from B to A (180 + B₁). On the graph I represented the bearing from B to A with the letter T.