Triangle calculator SSA

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Triangle has two solutions with side c=8.04439907611 and with side c=3.71333433997

#1 Obtuse scalene triangle.

Sides: a = 6.01   b = 2.5   c = 8.04439907611

Area: T = 5.02656813588
Perimeter: p = 16.55439907611
Semiperimeter: s = 8.27769953806

Angle ∠ A = α = 29.98880724774° = 29°59'17″ = 0.52333906011 rad
Angle ∠ B = β = 12° = 0.20994395102 rad
Angle ∠ C = γ = 138.0121927523° = 138°43″ = 2.40987625423 rad

Height: ha = 1.67224397201
Height: hb = 4.0210545087
Height: hc = 1.25495492618

Median: ma = 5.14327491367
Median: mb = 6.98993092422
Median: mc = 2.23879908755

Inradius: r = 0.60771866816
Circumradius: R = 6.01221679309

Vertex coordinates: A[8.04439907611; 0] B[0; 0] C[5.87986670804; 1.25495492618]
Centroid: CG[4.64108859472; 0.41765164206]
Coordinates of the circumscribed circle: U[4.02219953806; -4.46987488616]
Coordinates of the inscribed circle: I[5.77769953806; 0.60771866816]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0121927523° = 150°43″ = 0.52333906011 rad
∠ B' = β' = 168° = 0.20994395102 rad
∠ C' = γ' = 41.98880724774° = 41°59'17″ = 2.40987625423 rad




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6.01 ; ; b = 2.5 ; ; c = 8.04 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6.01+2.5+8.04 = 16.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.55 }{ 2 } = 8.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.28 * (8.28-6.01)(8.28-2.5)(8.28-8.04) } ; ; T = sqrt{ 25.26 } = 5.03 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.03 }{ 6.01 } = 1.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.03 }{ 2.5 } = 4.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.03 }{ 8.04 } = 1.25 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.01**2-2.5**2-8.04**2 }{ 2 * 2.5 * 8.04 } ) = 29° 59'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-6.01**2-8.04**2 }{ 2 * 6.01 * 8.04 } ) = 12° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.04**2-6.01**2-2.5**2 }{ 2 * 2.5 * 6.01 } ) = 138° 43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.03 }{ 8.28 } = 0.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.01 }{ 2 * sin 29° 59'17" } = 6.01 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.01   b = 2.5   c = 3.71333433997

Area: T = 2.3220002752
Perimeter: p = 12.22333433997
Semiperimeter: s = 6.11216716998

Angle ∠ A = α = 150.0121927523° = 150°43″ = 2.61882020525 rad
Angle ∠ B = β = 12° = 0.20994395102 rad
Angle ∠ C = γ = 17.98880724774° = 17°59'17″ = 0.31439510908 rad

Height: ha = 0.77220475048
Height: hb = 1.85660022016
Height: hc = 1.25495492618

Median: ma = 0.99547032733
Median: mb = 4.83765286727
Median: mc = 4.21216291621

Inradius: r = 0.3879601992
Circumradius: R = 6.01221679309

Vertex coordinates: A[3.71333433997; 0] B[0; 0] C[5.87986670804; 1.25495492618]
Centroid: CG[3.19773368267; 0.41765164206]
Coordinates of the circumscribed circle: U[1.85766716998; 5.71882981235]
Coordinates of the inscribed circle: I[3.61216716998; 0.3879601992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.98880724774° = 29°59'17″ = 2.61882020525 rad
∠ B' = β' = 168° = 0.20994395102 rad
∠ C' = γ' = 162.0121927523° = 162°43″ = 0.31439510908 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.01 ; ; b = 2.5 ; ; beta = 12° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 2.5**2 = 6.01**2 + c**2 -2 * 2.5 * c * cos (12° ) ; ; ; ; c**2 -11.757c +29.87 =0 ; ; p=1; q=-11.7573341608; r=29.8701 ; ; D = q**2 - 4pr = 11.757**2 - 4 * 1 * 29.87 = 18.7545065692 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 11.76 ± sqrt{ 18.75 } }{ 2 } ; ; c_{1,2} = 5.87866708041 ± 2.16532368072 ; ;
c_{1} = 8.04399076113 ; ; c_{2} = 3.71334339969 ; ; ; ; (c -8.04399076113) (c -3.71334339969) = 0 ; ; ; ; c>0 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6.01 ; ; b = 2.5 ; ; c = 3.71 ; ;

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6.01+2.5+3.71 = 12.22 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.22 }{ 2 } = 6.11 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.11 * (6.11-6.01)(6.11-2.5)(6.11-3.71) } ; ; T = sqrt{ 5.38 } = 2.32 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.32 }{ 6.01 } = 0.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.32 }{ 2.5 } = 1.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.32 }{ 3.71 } = 1.25 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.01**2-2.5**2-3.71**2 }{ 2 * 2.5 * 3.71 } ) = 150° 43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-6.01**2-3.71**2 }{ 2 * 6.01 * 3.71 } ) = 12° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.71**2-6.01**2-2.5**2 }{ 2 * 2.5 * 6.01 } ) = 17° 59'17" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.32 }{ 6.11 } = 0.38 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.01 }{ 2 * sin 150° 43" } = 6.01 ; ;




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