Two ships leave a port at the same time The first ship sails

Two ships leave a port at the same time. The first ship sails on a bearing of 52 degree at 17 knots (nautical miles per hour) and the second on a bearing of 322 degree at 22 knots. How far apart are they after 2.5 hours? Answer in nautical miles.

Solution

after 2.5 hrs,

first ship will travel d = 2.5*17 = 42.5 nautical miles

second ship will travel d = 2.5*22 = 55 nautical miles.

suppose they started from origin.

Then location of both ship after 2.5 hrs will be,

X (42.5 sin52, 42.5 cos52) = X (33.49,26.16)

Y(55 sin322, 55 cos322) = Y (-33.86 , 43.34)

Distance XY = sqrt((33.49-(-33.86))^2 + (26.16-43.34)^2)

XY = 69.48 nautical miles.