# maths

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Two planes take off from the same airport at the same time. One plane travels on a bearing S 12degreeW at 400 miles per hour. The other plane travels on a bearing N 75degreeE at 300 miles per hour. How far are the planes from each other 3 hours after takeoff?

• maths -

d1=3h * 400mi/h @ 258Deg=1200mi@258Deg.

d2 = 3h * 300mi/h @ 15deg=900km@15deg.

Da = d1 - d2 = Distance apart.
Da = 1200km@258 = 900km@15deg. =

X = hor.=1200cos258 - 900cos15=-1119mi.
Y=ver.= 1200sin258 - 900sin15=-1407mi

tanA = Y/X = -1407/-1119 = 1.2574.
A = 51.5 deg.
A = 51.5 + 180 = 231.5 Deg.

Da = -1119 / cos231.5 = 1798mi apart.

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