Question 1182010
Here's how to solve this problem:

1. **Visualize the Problem:** Draw a diagram.  Represent Sasquatch Point as S, Chupacabra Trailhead as C, and Muffin Ridge Observatory as M.  You'll have a triangle SMC.

2. **Angles:**
   * The hiker walks due west from S to C.
   * From C, she hikes N50°W to M. This means angle SCM is 90° + 50° = 140°.
   * From M, the bearing to S is S63°E. This means angle CMS is 63°.

3. **Find Angle SMC:** The sum of angles in a triangle is 180°.  So, angle SMC = 180° - (140° + 63°) = 180° - 203° = -23°. Since the angle cannot be negative we use 360 - 203 = 157. Therefore, angle SMC = 157°

4. **Law of Sines:** We can use the Law of Sines to find the distance SM (which we'll call 'x'). The Law of Sines states:

   a/sin(A) = b/sin(B) = c/sin(C)

   In our triangle:
   * SM / sin(SCM) = CM / sin(SMS) 
   * x / sin(140°) = 10 / sin(157°)

5. **Solve for x:**
   x = (10 * sin(140°)) / sin(157°)
   x ≈ (10 * 0.6428) / 0.3907
   x ≈ 16.45 miles

**Answer:** The hiker will have to walk approximately 16.5 miles to get from the Muffin Ridge Observatory to Sasquatch Point.