Airports A and B are 429 km apart on an eastwest line Jim fl

Airports A and B are 429 km. apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C, he flies 305 km. on a bearing of 128° 20\' to B.

How far is C from A?

Solution

Drop a perpendicular from C to the East - West line. Let us call the point where this line meets the East - West line D.

The angle CB makes with respect to the east - west line is: 180^o - (128^o20^\') = 51^o40\' = 51.67^o

so the distance covered horizontally along East - West line is: DB = 305cos51.67^o = 189.17 km

and total distance between A and B is 429 km.

therefore AD = AB - DB = 429 - 189.17 = 239.83 km

And angle made between AC and AB is 45^o  [North - East direction].

so, ACcos45^o = 239.83

therefore AC = 239.83/cos45^o = 339.17 km.