Need help finding an angle in degrees

• Jan 19th 2007, 08:10 AM
thedoge
Need help finding an angle in degrees
A map suggests that Atlanta is 731 mi in a direction of 4.90° north of east from Dallas. The same map shows that Chicago is 562 miles in a direction of 21.0° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.
magnitude

Now I've drawn this out and I get distance between dallas/chicago = 774 miles.

Now as far as the angles inside the triangle I used the law of sines.

sin(a)/A = sin(b)/B = sin(c)/C I know the answer is between 41.2 and 48.6 but I think I made a calculation error somewhere because I keep slightly getting the wrong answer.

Ive got less than one hour.
• Jan 19th 2007, 09:01 AM
Soroban
Hello, thedoge!

Your diagram must be off . . . We use the Law of Cosines.

Quote:

A map suggests that Atlanta is 731 mi in a direction of 4.90° north of east from Dallas.
The same map shows that Chicago is 562 miles in a direction of 21.0° west of north from Atlanta.
Find the displacement from Dallas to Chicago.

Code:

                    C *            :                         *          :                           * 562    :                             *      :                               * 21° :                                 *  :                               69° * :                       - - - - - - - * A                         4.9°  *                   731  *                   *             * 4.9°     D * - - - - - - - - - - - -

We have $\Delta CAD$ with: . $\angle CAD = 73.9^o,\:AC = 562,\:AD = 731$

Law of Cosines: . $DC^2\:=\:562^2 + 731^2 - 2(562)(731)\cos73.9^o \:=\:622,351.079$

Therefore: . $DC \;\approx\;788.89$ miles.

• Jan 19th 2007, 09:06 AM
thedoge
Too late to help on my homework, but you still helped me to understand the problem. Thank you.

I had figured my initial distance was incorrect, but it was graded correctly.