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Durabrand the Mountain Man

In this presentation, Mr. Shelden explores the problem of determining the distances between three mountains: Mt. R, Mt. B, and Mt. O. Leveraging the Triangle Sum Theorem and the Law of Sines, he derives crucial measurements such as the lengths of sides and angles within the triangles formed. After analyzing the geometry of the situation, he concludes that the distance from Mt. B to Mt. R is 38.5 miles, from Mt. R to Mt. O is also 38.5 miles, and from Mt. O to Mt. B is 44.1 miles. The entire perimeter amounts to 121.1 miles.

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Durabrand the Mountain Man

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Presentation Transcript

  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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