a Calculate to the nearest kilometre the distance between to

(a) Calculate, to the nearest kilometre, the distance between towns W and Y. (b) Calculate, to the nearest degree, the size of the angle marked theta. (c) Calculate, to the nearest kilometre, the distance between towns Y and Z.

Solution

in first triangle angle xwy = 180 - ( 58 + 90 )

= 32 degrees

now finding the length WY

applying law of sines on upper triangle XWY

32 / sin 58 = WY / sin 90

WY = 37.73

distance between towns W and Y is 38 kilometres

b) applying law of sines on bottom triangle WZY and finding angle WYZ

27 / sin Y = 37.73 / sin 90

sin Y = 27 / 37.73

angle WYZ = 45.7 degrees

now angle theta = 180 - ( 90 + 45.7 )

theta = 44 degrees

c) distance between towns Y and Z

applying law of sines

37.73 / sin 90 = YZ / sin 44

YZ = 26

so distance between towns Y and Z is 26 kilometres