An aeroplane flies from a town X on a bearing of N45E to another town Y, a distance 200km.it then changes course and flies to another town Z on the bearing of S60E.if Z is directly east of X, calculate, correct to three significant figures.a.the distance from X to Z b.the distance from Y to XZ

Answer 1

Please answer the question

Answer 2

(a) use the law of cosines.
I gotta go now, but I'll check on what you get when I return.

Answer 3

Hmmm. No work yet, I see. Oh, well. As it happens, I had not read the question carefully, so the law of cosines would not be of any use. Instead, use the law of sines. If we label the sides x,y,z opposite angles X,Y,Z, then by the law of sines, we have

y/sin105° = 200/sin30°
XZ = y = 386.37

If we label P the point where the altitude from Y meets XZ, then triangle YPZ is a 30-60-90 right triangle.
Again, using the law of sines,
x/sin45° = 200/sin30°
YZ = x = 282.84
So YP = x/2 = 141.42