Question 1182010: 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 10 miles along a bearing of N50°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S63°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquach Point, to the nearest tenth of a mile?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! 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.
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