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killaI9BI

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## Homework Statement

I've been stuck on this problem for hours. Any help you can provide is greatly appreciated.

From a lookout point, a hiker sees a small lake ahead of her. In order to get around it, she walks 4.5km in a straight line toward the end of the lake. She turns right making a 60° angle with her original path, and walks to a campsite 6.4km in the new direction. Determine her displacement from the lookout point when she has reached the campsite.

## Homework Equations

c

^{2}= a

^{2}+ b

^{2}-2ab cosθ

sin a/a = sin b/b

## The Attempt at a Solution

c

^{2}= 4.52 + 6.42 – 2(4.5)(6.4)cos60

c

^{2}= 20.25 + 40.96 – 28.8

c

^{2}= 32.41

c = 5.69km

sin θ = (sin 60/5.69) X 6.4

sin θ = 0.974

θ = 76.9°

θ = 90 – 77 = 13°

The hiker is 5.7km 13° above horizontal, right of her original heading from the lookout when she reached the campsite.

The book's answer is 5.8km, 18° away from the horizontal from the lookout.