Question

An airplane flies from a town X on a bearing of N45
0E to another
town Y, a distance of 200km. It then. Changes course and flies to
another town Z on a bearing of S60
0E. If Z is directly east of X, calculate, correct to 3 significant figures. a. the distance from X to Z
b. the distance from Y to XZ

Answer 1

a. the distance XZ = 200cos45° + (200 sin45°)tan60° = 200/√2 + 200/√2 * √3
b. 200 cos45° = 200/√2

Answer 2

All angles are measured CW from +y-axis.
a. cos45 = h/200.
h = 141.4 km.
sin45 = d1/200.
d1 = 141.4 km.
Tan60 = d2/141.4.
d2 = 245 km.
XZ = d1 + d2 = 141.4 + 245 = 386 km.

b. YZ^2 = d2^2 + h^2 = 245^2 + 141.4^2 = 80,019,
YZ = 283 km[120o] CW.





b.

Answer 3

in a diagram AB = 8km BC= 13km the bearing of A from B = 310 and the bearing of B from C is 230 calculate the distance AC the bearing of A and C