SOLUTION: A man walks due west for 4 km. He then changes direction and walks on a bearing of 197° until he is south-west of his starting point How far is he then from his starting point?

Question 1177475: A man walks due west for 4 km. He then
changes direction and walks on a bearing of
197° until he is south-west of his starting point
How far is he then from his starting point?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
After walking due west, he is at the point (-4,0)
A heading of 197 degrees means the angle is 73 degrees below the x-axis
Let A = tan(73)
Then the equation of the line is (using point-slope form) is:
y - 0 = tan(A)(x - -4) -> y = tan(A)(x + 4)
He walks until he is SW from his starting point, so we need to find the
intersection of this line with the line y = x
x = tan(A)x + 4tan(A) -> 4tan(A)/(1- tan(A)) = x = -5.7615 -> y = -5.7615
Thus he is sqrt((-5.7615)^2 + (-5.7615)^2) = 8.1479

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