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# A man on a horse rode 4km due south before turning and travelling 6.5km due west. The bearing the horse and man must travel on to return to

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A man on a horse rode 4km due south before turning and travelling 6.5km due west. The bearing the horse and man must travel on to return to their starting point is

math
Aug 12, 2014

#1
+3450
+8

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Aug 12, 2014

#1
+3450
+8

NinjaDevo Aug 12, 2014
#2
+98196
+5

We can use the inverse tangent to help us, here.

So we have

tan-1 (4/6.5) ≈ 31.6°

And the complement to this angle is (90 - 31.6) = 58.4°

So the bearing he needs to take to return to his starting spot is just........

N58.4°E

Here's a graph of the situation:

Aug 12, 2014
#3
+3450
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Ah I see, I as getting caught up of the "bearing" part.

I thought it meant distance to the starting point, but it really meant the angle.

Aug 12, 2014
#4
+98196
0

No prob, ND......"bearing" is a Trig topic.....however, your answer is useful, too. After all, knowing how far you might have to travel to get back to the starting point might be just as important as knowing the bearing to take to get there !!!!

I'll still give you some points for a good try!!

Aug 12, 2014