SOLUTION: Hello! Thank you in advance for taking the time to help me! The question is: Two planes take off from the same airport at the same time using different runways. One plane travel

Click here to see ALL problems on Triangles

Question 1129586: Hello! Thank you in advance for taking the time to help me!
The question is: Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing S15 degreesW at 350 miles per hour. The other plane travels on a bearing N75 degrees E at 250 miles per hour. How far are the planes from each other 3 hours after takeoff?
Answer: The distance is approximately _____ miles (round to the nearest mile as needed)
I've been stuck on this problem for nearly over an hour and a half now with countless pieces of paper with my work, however, every time i solve this, I get a different answer and not the right one. I am starting to get very frustrated with this so figured I could ask for some help on how to walk through this problem. Thank you!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing S15 degrees W at 350 miles per hour. The other plane travels on a bearing N75 degrees E at 250 miles per hour. How far are the planes from each other 3 hours after takeoff?
-----
S15 degrees W is an azimuth of 270-15 = 255 degrees
x coordinate after 3 hrs at 350 mph:: 3*350cos(255 deg) = -271.77
y coordinate after 3 hrs at 350 mph:: 3*350sin(255 deg) = -1014.22
---
N75 degrees E is an azimuth of 90-75 = 15 degrees
x coordinate after 3hrs at 350 mph:: 3*350cos(15 deg) = 1014.22
y coordinate aftere 3 hrs at 350 mph:: 3*350sin(15 deg) = 271.80
--------------
distance = sqrt[(1014.22+271.77)^2 + (1014.22+271.8)^2]
distance = sqrt[1651790.448+1653847.44] = 1818.14 miles
-----
Answer: The distance is approximately 1818 miles (round to the nearest mile as needed)