# Thread: Law of Cosine Word Problems

1. ## 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

2. 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

3. Hello, jordangiscool!

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

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

Draw line segment $\displaystyle AC.$

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

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

Got it?