1. ## Bearing/Navagation PreCal Problem

From city A to city B, a plane flies 650 miles at a bearing N48degreesE. From city B to city C the plane flies 810 miles at a bearing S36degreesE. Find the return distance from C to A and the bearing from C to A.

I'm unsure of if I use 36 degrees as the angle measure for B. I believe 42 degrees would be angle A's measurement. If this is correct, I got 711.5293 miles from city C to A using the Law of Sines. How would I go about finding the bearing from C to A?

Thanks!

2. Originally Posted by accordry
From city A to city B, a plane flies 650 miles at a bearing N48degreesE. From city B to city C the plane flies 810 miles at a bearing S36degreesE. Find the return distance from C to A and the bearing from C to A.

I'm unsure of if I use 36 degrees as the angle measure for B. I believe 42 degrees would be angle A's measurement. If this is correct, I got 711.5293 miles from city C to A using the Law of Sines. How would I go about finding the bearing from C to A?

Thanks!
First thing to do is sketch the figure. In geometry it is important that you have the correct figure or diagram....especially with bearings.

The figure would be a triangle ABC where
AB = 650 mi
BC = 810 mi
angle ABC = angle B = 48 +36 = 84 degrees

Why 48 +36?
Because at point B, if you drop a vertical line to signify the South axis, then the bearing of BA is S 48deg W ....just the opposite of the bearing of AB, which is given as N 48deg E.

So in the figure, there are two known sides and their included angle. So use the Law of Cosines to find the 3rd side.
(CA)^2 = (650)^2 +(810)^2 -2(650)(810)cos(84deg)

Now you can get the angle C by the Law of Sines:
650/ sinC = 984.14 /sin(84deg)
angle C = arcsin[650*sin(84) /984.14deg)
angle C = 41.06 deg, or, say, 41 degrees.

Then, for the bearing of CA,
here is one way,
draw a North-South crossline at point C.
it is easy to see now the bearing of CA.
it is N (36 +41 = 77) W....or N 77deg W -------answer.

3. Thanks sooo much! I actually think I understand it now.

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### bearing precal

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