Durabrand Durabrand the Mountain the Mountain

ManMan

Solution and Solution and PresentationPresentation

by Mr. Sheldenby Mr. Shelden

Here’s our problemHere’s our problem

What are the distances between the mountains?

We know…

• ∠BFR = 130°• ∠OFR = 130°

Mt. R

Flag

Mt. O

Mt. B

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

Mt. B

Mt. O

70°

F-lag

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

R

F

B

35°

130°

13

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

Mt. O

Mt. BFlag

Last Triangle - IsocelesLast 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. O

Mt. B

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. O

Mt. B

Mt. R

QuestionsQuestions

• 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?