SOLUTION: Two ships leave port at noon. One ship's speed is 15 km/h on a heading of 75 degree. The other ship's speed is 24 km/h on a heading of 155 degree. How far apart are they at 3pm and

Question 1073792: Two ships leave port at noon. One ship's speed is 15 km/h on a heading of 75 degree. The other ship's speed is 24 km/h on a heading of 155 degree. How far apart are they at 3pm and what is the bearing of each from the other?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two ships leave port at noon. One ship's speed is 15 km/h on a heading of 75 degree.
The other ship's speed is 24 km/h on a heading of 155 degree.
:
Find the distance they traveled in 3 hrs
1st ship dist: 3 * 15 = 45 km
2nd ship dist: 3 * 24 = 72 km
Find the angle between the paths of these two ships.
155 - 75 = 80 degrees between the two ship's paths.
:
How far apart are they at 3pm and what is the bearing of each from the other?
Draw this out as triangle, use law the of cosines to find the distance between two ships
a = distance between the ships
A = 80 degrees
b = 45
c = 72
a^2 = b^2 + c^2 - 2(bc)*cos(80)
a^2 = 45^2 + 72^2 - 2(45*72)*.173648
You do the math, I got
a = 78.00 km between the ships at 3 pm
:

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