# Math Help - Bearing problem

1. ## Bearing problem

I do not need this problem solved. Im just not sure how the drawing of this problem should look.
If someone could show me how it should look that would be greatly appreciated.

The bearing of a lighthouse from a ship was found to be N 37�� E. After the ship sailed 2.5 mi due south, the new bearing was N 25�� E. Find the distance between the ship and the lighthouse at each location.

2. Originally Posted by Brndo4u
I do not need this problem solved. Im just not sure how the drawing of this problem should look.
If someone could show me how it should look that would be greatly appreciated.

Distance Between a Ship and a Lighthouse ship was found to be N 37􏰂 E. After the ship sailed 2.5 mi due south, the new bearing was N 25􏰂 E. Find the distance between the ship and the lighthouse at each location.
The bearing of a lighthouse from a
apologize for the "mouse" tracks ...

3. Where does the N 37 E go in the drawing. I edited the problem it was worded wrong the first time.

4. Hello, Brndo4u!

$\text{The bearing of a lighthouse from a ship was found to be }N\,37^o\,E.$
$\text{After the ship sailed 2.5 mi due south, the new bearing was }N\,25^o\,E.$
$\text{Find the distance between the ship and the lighthouse at each location.}$
Code:
    N                       ♠ L
:                   * *
:               *12o*
:           *     *
: 37o   *       *
:   *         *
A ♥ 143o      *
:         *
:       *
2.5 : 25o *
:   *
: *
B ♥

The lighthouse is at $\,L.$

When the shp is at $\,A,\:\angle N\!AL = 37^o.$

The ship sails 2.5 miles to $\,B\!:\:AB = 2.5;\;\angle NBL = 25^o$

We see that $\angle LAB = 143^o,\,\text{ hence: }\:\angle ALB = 12^o$

In $\Delta ALB$, use the Law of Sines:

. . $\displaystyle \frac{AL}{\sin25^o} \:=\:\frac{2.5}{\sin12^o} \quad\Rightarrow\quad AL \:\approx\:5.08\text{ miles.}$

. . $\displaystyle \frac{BL}{\sin143^o} \:=\:\frac{2.5}{\sin12^o} \quad\Rightarrow\quad BL \:\approx\:7.24\text{ miles.}$