# Math Help - Trig Help. =]

1. ## Trig Help. =]

A ship is sailing due North. At a certain point the bearing of a lighthouse that is 12 miles away is found to be 39Degrees East of due North. Later the bearing is determined to be 44Degrees East of due North. How far, to the nearest tenth of a mile, has the ship traveled?

I don't understand how to even sketch this out. =[

2. Hello, Helltech!

A ship is sailing due North. At a certain point the bearing of a lighthouse
that is 12 miles away is found to be N 39° E.
Later the bearing is determined to be N 44° E.
How far, to the nearest tenth of a mile, has the ship traveled?
Code:
      N                           o L
|                       * *
|                    *  *
|                 * 5°*
|              *    *
|           *     *
|        *      *
| 44° *       *
|  *        * 12
B o 136°    *
|       *
x |     *
|39°*
| *
A o

The lighthouse is at $L.$

When the ship is at $A,\:\angle NAL = 39^o\text{, and }AL = 12$

When the ship is at $B,\:\angle NBL = 44^o\quad\Rightarrow\quad \angle LBA = 136^o$

We want: . $x \:=\:AB$

In $\Delta ABL,\;\angle BLA \:=\:180^o - 136^o - 39^o \:=\:5^o$

Law of Sines: . $\frac{x}{\sin5^o} \:=\:\frac{12}{\sin136^o} \quad\Rightarrow\quad x \:=\:\frac{12\sin5^o}{\sin136^o} \:=\:1.505587433$

Therefore, the ship traveled about 1.5 miles.