Trigonometry question

[bazbeatz]

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

[stapel_eliz]

I have tried using the cosine formula....

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

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.

[bazbeatz]

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