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Durabrand the Mountain Man

Durabrand the Mountain Man. Solution and Presentation by Mr. Shelden. Here’s our problem. What are the distances between the mountains? We know… ∠BFR = 130° ∠OFR = 130°. Mt. R. Flag. Mt. B. Mt. O. Disclaimer: Not drawn to scale. After Durabrand’s hike we know…. ∠BRO=70°

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Durabrand the Mountain Man

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  1. Durabrand the Mountain Man Solution and Presentation by Mr. Shelden

  2. Here’s our problem What are the distances between the mountains? We know… • ∠BFR = 130° • ∠OFR = 130° Mt. R Flag Mt. B Mt. O Disclaimer: Not drawn to scale

  3. After Durabrand’s hike we know… • ∠BRO=70° • Since F is in the middle, it bisects ∠BRO. Therefore ∠BRF = 35° and ∠FRO = 35° • Also, FR = 13 miles Mt. R 70° Mt. B F-lag Mt. O

  4. Three pieces of info? • We know two angles and one side. • Triangle sum theorem ∠B=15° • Law of Sines BR = 38.5 BF = 28.8 35° R 13 130° F B

  5. Congruent Triangles? • ∠BFR = 130° = ∠OFR • ∠FRB = 35 ° = ∠FRO • FR = 13 = FR • ∆BFR is congruent to ∆OFR by ASA • Therefore BR = 38.5 = RO BF = 28.8 = FO Mt. R Flag Mt. B Mt. O

  6. Last Triangle - Isoceles • We know BF and FO • They’re the same, so ISOCELES!!!!!! • Since a circle has 360°, ∠F = 100° • Triangle sum theorem ∠B = 40° = ∠O • Law of Sines BO = 44.1 F-lag Mt. B Mt. O

  7. Solution!! • The distance from Mt. B to Mt. R is 38.5, the same as from Mt. R to Mt. O. • From Mt. O to Mt. B it’s 44.1 miles • That’s a perimeter of 121.1 miles. Mt. R Mt. B Mt. O

  8. Questions • Do hikers really do things like this when they’re bored and alone on the trail? • Are these distances accurate for a hiker? • Did you have to use Law of Sines on the last triangle since it was isoceles? • Was this an effective presentation?

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