SOLUTION: A man walks due west for 4 km he then change direction and walk on a bearing of 197° until he is southwest of his starting point how far is he then his starting point
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Question 1175814: A man walks due west for 4 km he then change direction and walk on a bearing of 197° until he is southwest of his starting point how far is he then his starting point
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
A bearing of 197 degrees is 17 degrees west of south.
After walking 4 miles west from his starting point, his displacement in the x direction is 4 miles west and his displacement in the y direction is 0.
In walking a distance d at an angle 17 degrees west of south, his displacement in the x direction is (west), and his displacement in the y direction is (south).
So his total displacement is west and south.
He is southwest of his starting point when his displacements west and south are equal.
That is not an equation you are going to solve manually; use a calculator.
Then remember that the question asks for how far he is from his starting point. The solution to the equation you solved is his displacement in each of the x and y directions; so his distance from his starting point is that displacement multiplied by the square root of 2.
(To check your calculations, note my answer was a bit over 8km....)
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