Trigonometry question

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
bazbeatz
Posts: 4
Joined: Sun Jun 07, 2009 5:48 pm
Contact:

Trigonometry question

Postby bazbeatz » Sun Jun 07, 2009 5:55 pm

Hi,

I am trying to teach myself trig from a book and have come across the following question that I cannot seem to get the right answer for...

Two ships leave port at the same time. The first steams on a bearing 135 degrees at 18km/h and the second on a bearing of 205 degrees at 15km/h. Calculate the time that will have elapsed when they are 86km apart.

The book gives the answer as 4.51 hours but I can't get this.

I have tried using the cosine formula and end up with a quadratic equation which when solved does not give me the correct answer. Am I overcomplicating the method?

Thanks for any help

User avatar
stapel_eliz
Posts: 1733
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sun Jun 07, 2009 6:14 pm

bazbeatz wrote:I have tried using the cosine formula....

Would this be the Law of Cosines? What were your steps? What did you get up with?

bazbeatz wrote:Two ships leave port at the same time. The first steams on a bearing 135 degrees at 18km/h and the second on a bearing of 205 degrees at 15km/h. Calculate the time that will have elapsed when they are 86km apart.

Let A be the starting point, with the first ship heading toward B and the second heading toward C. Let a be the side opposite vertex A; let b and c be defined similarly. Then we get:

. . . . .862 = (18t)2 + (15t)2 - 2(18t)(15t)cos(70)

Solving (starting by factoring the t2 out of the right-hand side), you should get the book's answer.

:wink:

bazbeatz
Posts: 4
Joined: Sun Jun 07, 2009 5:48 pm
Contact:

Re: Trigonometry question

Postby bazbeatz » Sun Jun 07, 2009 10:49 pm

Thanks. Looking back through my working I was close as I had the formula you state. However I was going wrong in the way I was factoring (18t*15t =270t instead of =270t^2) which was leading me to all sorts of wrong solutions.

Many thanks for your speedy response


Return to “Trigonometry”

cron