need help with another bearing question?

[thatdumbstudent]

Alice operates a charter flight service for country Victoria. She is planning a round trip from
her base at Bendigo to Shepparton, Ballarat and then returning to Bendigo.

If a vertical line points North  find the bearing that Alice must fly from:
i Bendigo to Shepparton ii Shepparton to Ballarat iii Ballarat to Bendigo

so the distance from bendigo to shepparton is 106.5km and from sheppartan to ballarat its 177.9km. ballarat to bendigo is 85km. I've tried using the cosine rule but i couldn't figure it out... much help would be appreciated!

[^^^111^^^]

Alice operates a charter flight service for country Victoria. She is planning a round trip from
her base at Bendigo to Shepparton, Ballarat and then returning to Bendigo.

If a vertical line points North  find the bearing that Alice must fly from:
i Bendigo to Shepparton ii Shepparton to Ballarat iii Ballarat to Bendigo

so the distance from bendigo to shepparton is 106.5km and from sheppartan to ballarat its 177.9km. ballarat to bendigo is 85km. I've tried using the cosine rule but i couldn't figure it out... much help would be appreciated!

You are right about using the cosine rule, since we now the length of all three sides but not the angle. So, by transposing the cosine rule to find the angle, we get the formula:

cos C = (a² + b² - c²) / 2ab.
cos B = (a² - b² + c²) / 2ac.
cos A = ( b² + c² - a²) / 2bc.
Now it is simple. Plug in the sides of the triangle to the formula and you are good to go. Let me do one for you as a model:

i) Bendigo to Shepparton
1. Draw a labelled triangle, with side lengths.Let 177.9 km be side a, 106.5km be side b and 85km be side c. 
2. By using the formula a^2 + b^2 - c^2 = 35765.66km. Divide that by 2ab or 2(177.9)(106.5). Then find the angle by finding the inverse of cosine to the value you got from step 2.