# Durabrand the Mountain Man - PowerPoint PPT Presentation

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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

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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°

• 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?

• 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?

• ∠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

• 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!!

• 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

• 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?