SOLUTION: Airports A and B are 448 km apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C he flies 322 km on a bearing of 125(degrees)20(seconds) to B

Algebra ->  Trigonometry-basics -> SOLUTION: Airports A and B are 448 km apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C he flies 322 km on a bearing of 125(degrees)20(seconds) to B      Log On


   

Question 1008830: Airports A and B are 448 km apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C he flies 322 km on a bearing of 125(degrees)20(seconds) to B. How far is C from A?
The answer is 263 km, but I am having difficulty figuring out how to put the triangle together on bearing questions.
Thanks
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's a good reference that you should look at because it has good information for how to set up and solve these types of problems.

take the time to look at it.

it will be worth your while.

https://www.youtube.com/watch?v=qYKsli4L3RM

your diagram is going to look like this:

$$$

basically a bearing without a direction is taken from the north south line where one side of the angle is the north south line and the other side of the angle is found by rotating clockwise the required number of degrees.

the angle is shown on the diagram as angle ECB.

the point E is added to the north south line on the top of the diagram for easy angle reference.

that angle is 125 degrees 20 minutes.

the supplement of that angle is 54 degrees 40 minutes which becomes the angle insice the triangle formed by the north south line and the horizontal line between point A and B.

you wind up with two right triangles.

on the left is right triangle ACD and on the right is right triangle CBD.\

use cosine of 54 degrees 40 minutes to find the length of CD.

use sine of 54 degrees 40 minutes to find the length of DB.

subtract DB from 448 to get the length of AD.

use pythagorus to find the length of AC.

54 degrees 40 minutes is dequivalent to 54 degrees plus 40/60 degrees which is equjal to 54.66667 degrees.

use your calculator to obtain the appropriate trig measurements.