# Law of Cosine Word Problems

• Jul 12th 2009, 05:01 PM
jordangiscool
Law of Cosine Word Problems
A plane flies 810 miles from A to B with a bearing of N 75 degrees E. Then it flies 648 miles from B to C with a bearing of N 32 degrees E. Find the straight-line distance and bearing from C to A
• Jul 13th 2009, 03:20 AM
sa-ri-ga-ma
Quote:

Originally Posted by jordangiscool
A plane flies 810 miles from A to B with a bearing of N 75 degrees E. Then it flies 648 miles from B to C with a bearing of N 32 degrees E. Find the straight-line distance and bearing from C to A

The angle between AB and AC is 180 - 75 + 32 degrees
• Jul 13th 2009, 06:08 AM
Soroban
Hello, jordangiscool!

Quote:

A plane flies 810 miles from A to B with a bearing of N 75° E.
Then it flies 648 miles from B to C with a bearing of N 32° E.
Find the straight-line distance and bearing from C to A

Code:

                          Q    o C                           :    *                           :32°*                           :  *                           : *       P              105° |*       :                  o B       :              *  :       :          *  75° :       : 75°  *          :       :  *              R     A o

The plane flies from $A$ to $B\!:\;\;AB \,=\,810$
. . $\angle PAB \,=\, 75^o \,=\,\angle ABR \quad\Rightarrow\quad \angle ABQ \,=\,105^o$

Then it flies from $B$ to $C\!:\;\;BC \,=\,648$
. . $\angle QBC \,=\,32^o \quad\Rightarrow\quad \angle ABC \,=\,137^o$

Draw line segment $AC.$

We have . $\Delta ABC\!:\;\;AB = 810,\;BC = 648,\;\angle B = 137^o$

Law of Cosines: . $AC^2 \;=\;AB^2 + BC^2 - 2(AB)(BC)\cos B$

Got it?