Question

An aero plane flies from a town X on a bearing of N45°E to another town Y, a distance of 200km. it then changes course and flies to another town Z on a bearing of S60°E. If Z is directly to east of X, calculate,
(a) Draw a comprehensive diagram that illustrate the information above
(b) The distance from X to Z
(c) The distance from Y to XZ

Answer 1

using the law of sines,
(b) XZ/sin105° = 200/sin30°
(c) 200 sin45°

Answer 2

To TAKE a bearing on something, like a lighthouse bears northeast.
You fly or sail or walk on a HEADING.
Math text writers do not do navigation.
Anyway
how far east of x is y? 200 sin 45 call that a = 141.4

how far east of y is z?
well y is 200 cos 45 = 141.4 north of x (that is part c by the way)
so we must go 141.4 south to get to y
that means tan 60 = b/141.4 = 1.732
so b (east distance yz) = 244.9
a+b = x to z east = 386.3 ( part b)