SOLUTION: Two ships leave a port, sailing at 16 km/h and 12 km/h. The angle between their directions of travel from the port is 40°. How far apart are the ships after 3 hours? Include a diag

Algebra ->  Trigonometry-basics -> SOLUTION: Two ships leave a port, sailing at 16 km/h and 12 km/h. The angle between their directions of travel from the port is 40°. How far apart are the ships after 3 hours? Include a diag      Log On


   

Question 1038063: Two ships leave a port, sailing at 16 km/h and 12 km/h. The angle between their directions of travel from the port is 40°. How far apart are the ships after 3 hours? Include a diagram.
16(3)=4
12(3)=36
c^2 = 48^2+36^2-2(48)(36)cos40°
c^2 = 2304+1296-2647.45
c^2 = 952.55
c = 30.9
The answer should be 84. Where in the world am I going wrong?
Thank you
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is correct.
It's not 84.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You picked Law Of Cosines to describe the situation. You just need to know if you set your equation correctly, and then the rest is mostly arithmetic.

R*T=D, for any single direction.

c%5E2=%2816%2A3%29%5E2%2B%2812%2A3%29%5E2-2%2A16%2A3%2A12%2A3%2Acos%2840%29

c%5E2=48%5E2%2B36%5E2-2%2A48%2A36%2Acos%2840%29-----like what you show in your second step too.

c%5E2=2304%2B1296-3456%2Acos%2840%29

c%5E2=3600-3456%2Acos%2840%29

c%5E2=3600-2647.44

c%5E2=952.55

c=30.86------Or close-enough to what you found.