An aeroplane flies from a town X an a bearing of N45°E to another town Y,a distance of 200km.It then change course and flies to another town Z on a bearing of N60°E.If Z is directly east of X,Calculate and correct to 3s.f. (i)the distance from X to Y (ii)the distance from Y to XZ
I assume that Z is N60E of X, not Y.
In x-y coordinates, if X is at (0,0) then
XZ is the line y = 1/√3 x, or in general form,
x - √3 y + 0 = 0
so
(i) clearly, 200 km
(ii) the distance from (h,k) to Ax+By+C=0 is
|Ah+Bk+C|/√(A^2+B^2)
so since Y is at (100√2,100√2) just plug in your numbers