Question

-A man moves from a point X on a bearing of 068 to a point Y 400m away. He then moves from the point Y on a bearing 120 to a point z which 250 may. Calculatethe disatnce

Answer 1

588 m

Explanation:

The Law of Cosines is useful for finding the distance unknown distance 'c' when triangle sides 'a' and 'b' and the angle C between them are known.

c = √(a² +b² -2ab·cos(C))

c = √(400² +250² -2(400)(250)cos(128°)) ≈ 587.905 . . . m

Point Z is about 588 meters from the starting point.

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Additional comment

It is often useful to use (x, y) = (North, East) coordinates in such calculations. This lets the calculator use distance and bearing directly. It looks "backward" on a coordinate plane, but the math works out. If you flip the figure over the line y=x, it will correspond to what you expect to see on a map.