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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

Durabrand the Mountain Man

Solution and Presentation

by Mr. Shelden


Here s our problem
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
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


Three pieces of info
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


Congruent triangles
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


Last triangle isoceles
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


Solution
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


Questions
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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