Hi, I am really stuck on this math question:?

I'm gonna have to agree with la console, because he has the right answer...I found this question because I had just answered it on a math question :), LOL

Recall: s = d/t → where s is the speed, d is the distance, t is the time

Speed of ship No.1: 18 km/h. After 2 hours: OA = 2 * 18 = 36 km

Speed of ship No.2: 26 km/h. After 2 hours: OB = 2 * 26 = 52 km

AB² = BC² + AC²

AB² = [OB - OC]² + AC²

AB² = [OB - OC]² + AC² → where: OC = OA.cos(39)

AB² = [OB - OA.cos(39)]² + AC² → where: AC = OA.sin(39)

AB² = [OB - OA.cos(39)]² + OA².sin²(39)

AB² = OB² - 2.OB.OA.cos(39) + OA².cos²(39) + OA².sin²(39)

AB² = OB² - 2.OB.OA.cos(39) + OA².[cos²(39) + sin²(39)] → recall: cos²(x) + sin²(x) = 1

AB² = OB² - 2.OB.OA.cos(39) + OA² → where: OB = 52 km

AB² = 52² - 104.OA.cos(39) + OA² → where: OA = 36 km

AB² = 52² - 3744.cos(39) + 36²

AB² = 4000- 3744.cos(39)

AB² ≈ 1090.3655

AB ≈ 33.0206 km

That ship has sailed.

if they are both going on the same course.

their difference in speeds is 26-18= 8 KM/h

after two hours they are 8*2=16 Km apart.

Suppose the ships start from point O; they will reach point

A & point B after 2 hrs. The problem is to find AB. After 2 hrs

ship A has traveled 36 km;

ship B has traveled 52 km.

By the cosine rule:

AB=sqr[36^2+52^2-2(36)(52)cos(39*)]

=>

AB=sqr(1090.36552)~33 km.

Using the cosine rule for a triangle the ships are 33.02 km apart

Two ships leave a port, sailing 18 km/h and 26 km/h. 

Their angle between their directions of Travel from the port is 39°. 

The ships are 33.02 km apart after 2 hours.

After two hours ,each ship has travelled 36 km and 52 km . Their angle is 39 degrees. 

Use the Cosine rule, which us 

a^2 = b^2 + c^2 -2bcCosA 

a^2 = 36^2 + 52^2 - 2(36)(52)Cos(39) 

a^2 = 1296 + 2704 - 3722(0.777145...) 

a^2 = 1296 + 2704 - 2892.53....

a^2 = 1107.46... 

a = sqrt(1107.46...)

a = 33.278... km 

After 2 hours the two ships have sailed a distance of 36 km and 52 km respectively

The angle between them is maintained at 39°

If we think of the two ship's directions as two sides of a triangle, then the third side is the distance between them at this time. This side, d is opposite the 39° angle. So, using the 'cosine rule' we have:

d² = 36² + 52² - 2(36)(52)cos39°

so, d² = 4000 - 3744cos39°

=> d² = 1090.36552

Hence, d = 33.0 km

:)>

If it's after 2 hours

then one of them has travelled 36km and the other one 52km

So ..

You have a triangle

and you know that 2 of the sides are 36km and 52km

and the angle between those 2 sides is 39 degrees

and you need to work out the length of the third side.

Over to you ....

So you need the cosine rule as the others have now shown

which is

The length of the side you want, squared

EQUALS

the length of the other two sides, both squared, and added together

minus

the length of the other two sides multiplied together, times two 

times the cosine of the angle opposite the side you want to work out.

OR you could just draw it to scale and measure !