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A hiker starts walking due west from Sasquatch Point and gets to the Chupacabra Trailhead before she realizes that she hasn't reset her pedometer. From the Chupacabra Trailhead she hikes for 5 miles along a bearing of N55°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S65°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquatch Point?

User Yardboy
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1 Answer

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Final answer:

The distance from Muffin Ridge Observatory to Sasquatch Point can be determined by trigonometric methods, forming a right-angled triangle with the two given bearings, but a numeric answer requires additional data or specific measurements which are not provided.

Step-by-step explanation:

The student seeks to calculate the distance needed to walk from the Muffin Ridge Observatory straight back to Sasquatch Point using the bearing of S65°E. To solve this, we need to apply trigonometric principles to identify the displacement between the two points, which can be visualized as a triangle where the legs represent the two stages of the hiker's journey and the hypotenuse represents the direct path back to the starting point. Since the hiker walked from the Chupacabra Trailhead to the Muffin Ridge Observatory on a bearing of N55°W for 5 miles, and the bearing from the observatory back to the starting point is S65°E, these directions form a right-angled triangle.

Using the Law of Sines or the Pythagorean theorem, we can determine the length of the side opposite the right angle (the hypotenuse in this case), which represents the distance from the Muffin Ridge Observatory to Sasquatch Point. However, without specific measurements or additional data points such as the coordinates of Sasquatch Point and Muffin Ridge Observatory, we cannot provide a numeric answer. If the angles provided are presumed to perfectly form a right triangle, then trigonometric functions such as tangent could be used. Otherwise, a direct measurement or more comprehensive trigonometric analysis would be required.

User SwK
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