Question

I know I posted this before,but I did not learn it your way .....instead I drew a picture and use the law of cosines....is there a way you can show me the work using law of cosines??

A plane flies 30 mi on a bearing of 200 degrees and then turns and flies 40 mi on a bearing of 10 degrees. Find the resultant displacement vector as a distance and bearing.

Answer 1

sure,
After sketching in all the angles, and doing some arithmetic, I have a triangle with sides
30 and 40 and the angle between them as 10°
let the resultant be R
R^2 = 30^2 + 40^2 - 2(30)(40)cos10°
= 900+1600-2400cos10°
= 136.46..
R = √136.46
= 11.68 , which I believe I had before

for the angle, let Ø be the obtuse angle
sinØ/40 = sin10°/11.68
sinØ = 40sin10°/11.68 = .5947
Ø = 36.5° or 143.5°
but it is obviously obtuse,
so the bearing is 143.5 + 200 = 343.5°

I can't recall what I had in the other solution

Answer 2

Well if you add the sin and cosine you form an equilateral triangle, then you take the area of the triangle and form a helix,and the area of that 4. then you take the 4 cosine to that and add it to adjacent side. answer is 5