An aeroplane flies from a town x on a bearing of N45degreeE to another town Y a distance of 200 km. It then changes course and flies to another town z on a bearing of S60degreeE. If z is directly east of x, calculate, to 3 significant figures, (a) the distance from x to z
(b) the distance from y to xz
Answers
Given : An aeroplane flies from a town x on a bearing of N45degreeE to another town Y a distance of 200 km.
It then changes course and flies to another town z on a bearing of S60degreeE.
z is directly east of x,
To Find : the distance from x to z
Solution:
N45degreeE => 45° towards East from North
Distance between xy = 200 km
Hence y is 200sin45° North from x and 200cos45° east from x
hence y is 100√2 km North from x and 100√2 km East of x
S60degreeE => 60° towards East from South
Let say Distance between y and z is A km
Acos60° in south = 100√2 km North as x and z are in same horizontal line
A(1/2) = 100√2 => A = 200√2 km
Distance toward East = ASin60° = 200√2 (√3 / 2) = 100√6 km
Distance from x to z = 100√2 + 100√6 km
= 386 km to 3 significant figures
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