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Solve the triangle using Law of Sines

by Zachary
(CA, USA)











































How do i find all possible triangles that satisfy the given conditions?

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May 22, 2012
Solve the triangle using Law of Sines
by: Staff


Question:

by Zachary
(CA, USA)

How do i find all possible triangles that satisfy the given conditions?


Answer:

Law of Sines

a/(Sin A) = b/(Sin B) = c/(Sin C)



a/(Sin A) = b/(Sin B)

72/(Sin 21°) = 103/(Sin B)

Sin B = 103*(Sin 21°) / 72

Sin B = 103*(0.3583679495453) / 72

Sin B = 0.5126652611551

∠B = Sin⁻¹(0.5126652611551)

∠B = 30.8415250916575°



∠C = 180° - ∠A - ∠B

∠C = 180° - 21° – 30.8415250916575°

∠C = 128.1584749083425°

∠C = 128.2°


a/(Sin A) = c/(Sin C)


72/(Sin 21°) = c/(Sin 128.2°)

c = (Sin 128.2°) *72/(Sin 21°)


c = (0.7858568931754) *72/(0.3583679495453)

c = 157.887155869882


∠A₁ = 21°
a₁ = 72

∠B₁ = 30.8°
b₁ = 103

∠C₁ = 128.2°
c₁ = 157.9

a₁/(Sin A₁) = b₁/(Sin B₁) = c₁/(Sin C₁)

a₁/(Sin A₁) = 72/(Sin 21°) = 200.9108238930242
b₁/(Sin B₁) = 103/(Sin 30.8415250916575°) = 200.9108238930173
c₁/(Sin C₁) = 157.887155869882/(Sin 128.1584749083425°) = 200.7963581230925



∠B₂ = 180° - 30.8415250916575° = 149.1584749083425°


∠C₂ = 180° - ∠A₂ - ∠B₂

∠C₂ = 180° - 21° – 149.1584749083425°


∠C₂ = 9.8415250916575°

∠C₂ = 9.8°


72/(Sin 21°) = c₂/(Sin 9.8415250916575°)

c₂ = (Sin 9.8415250916575°) *72/(Sin 21°)


c₂ = (0.1709236283535) *72/(0.3583679495453)

c₂ = 34.3404069952868



∠A₂ = 21°
a₂ = 72

∠B₂ = 180° - 30.8415250916575° = 149.1584749083425°
b₂ = 103

∠C₂ = 9.8415250916575°
c₂ = 34.3404069952868



∠A₂ = 21°
a₂ = 72

∠B₂ = 149.2°
b₂ = 103

∠C₂ = 9.8°
c₂ = 34.3



a₂/(Sin A₂) = b₂/(Sin B₂) = c₂/(Sin C₂)

a₂/(Sin A₂) = 72/(Sin 21°) = 200.9108238930242
b₂/(Sin B₂) = 103/(Sin 149.1584749083425°) = 200.9108238930173
c₂/(Sin C₂) = 34.3404069952868/(Sin 9.8415250916575°) = 200.9108238930011



>>> the final answer is:

**Triangle 1


∠A₁ = 21°
a₁ = 72

∠B₁ = 30.8°
b₁ = 103

∠C₁ = 128.2°
c₁ = 157.9


**Triangle 2


∠A₂ = 21°
a₂ = 72

∠B₂ = 149.2°
b₂ = 103

∠C₂ = 9.8°
c₂ = 34.3




Thanks for writing.

Staff
www.solving-math-problems.com



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