# Law of Sines Word Problem - Ambiguous Case

• Dec 5th 2009, 02:51 PM
maryanna91
Law of Sines Word Problem - Ambiguous Case
Here's the word problem:

A ship is headed due north at a constant 24 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 22 miles per hour, in what direction are the currents running?

I know there's supposed to be two answers but I just keep getting to a point where Im not even sure what angle it is that Im looking for. Any help would be great :)
• Dec 6th 2009, 04:52 PM
Lucio Carvalho
help for the problem
Hello Maryanna,
First of all, sorry about my weak English (My official language is Portuguese).
In annexe, I show you my point of view about the problem.
I hope you understand!
Bye!
• Dec 6th 2009, 05:25 PM
maryanna91
Thanks so much! I really appreciate your help! :)
• Dec 7th 2009, 06:12 AM
aidan
Quote:

Originally Posted by maryanna91
Here's the word problem:

A ship is headed due north at a constant 24 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 22 miles per hour, in what direction are the currents running?

I know there's supposed to be two answers but I just keep getting to a point where Im not even sure what angle it is that Im looking for. Any help would be great :)

Lucio Carvalho has shown 1 solution.

The attached image is rough. It is not to scale.
It was quickly drawn & scanned.
This doesn't solve it, but the image shows the other case.

You have a triangle with two known sides and 1 known angle.
Use the $\text{Sine Law}$ to get the answer.

$
\dfrac{\sin\theta}{24} \, = \, \dfrac{\sin(15deg)}{22}
$

$
\sin\theta \, = \, 24 \dfrac{\sin(15deg)}{22}
$
(get the arcsin of $\theta$ in degrees.)

The direction of the current: $\theta + 15$

NOTE: Theta can also take the value $180 - \theta$ which will give the result as depicted by Lucio Carvalho.