Triangle calculator SSA

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Triangle has two solutions with side c=52.30438976695 and with side c=1.31992133488

#1 Obtuse scalene triangle.

Sides: a = 35   b = 34   c = 52.30438976695

Area: T = 588.3555203805
Perimeter: p = 121.304389767
Semiperimeter: s = 60.65219488348

Angle ∠ A = α = 41.42991285101° = 41°25'45″ = 0.72330746987 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 98.57108714899° = 98°34'15″ = 1.72203862541 rad

Height: ha = 33.62202973603
Height: hb = 34.60991296356
Height: hc = 22.4987566339

Median: ma = 40.49219603837
Median: mb = 41.12660119111
Median: mc = 22.50772337737

Inradius: r = 9.7010516061
Circumradius: R = 26.44773050566

Vertex coordinates: A[52.30438976695; 0] B[0; 0] C[26.81215555092; 22.4987566339]
Centroid: CG[26.37218177262; 7.49991887797]
Coordinates of the circumscribed circle: U[26.15219488348; -3.94215120071]
Coordinates of the inscribed circle: I[26.65219488348; 9.7010516061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.571087149° = 138°34'15″ = 0.72330746987 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 81.42991285101° = 81°25'45″ = 1.72203862541 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 = 35 ; ; b = 34 ; ; c = 52.3 ; ;

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

p = a+b+c = 35+34+52.3 = 121.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 121.3 }{ 2 } = 60.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.65 * (60.65-35)(60.65-34)(60.65-52.3) } ; ; T = sqrt{ 346161.85 } = 588.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 588.36 }{ 35 } = 33.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 588.36 }{ 34 } = 34.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 588.36 }{ 52.3 } = 22.5 ; ;

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{ 35**2-34**2-52.3**2 }{ 2 * 34 * 52.3 } ) = 41° 25'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 34**2-35**2-52.3**2 }{ 2 * 35 * 52.3 } ) = 40° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 52.3**2-35**2-34**2 }{ 2 * 34 * 35 } ) = 98° 34'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 588.36 }{ 60.65 } = 9.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 41° 25'45" } = 26.45 ; ;





#2 Obtuse scalene triangle.

Sides: a = 35   b = 34   c = 1.31992133488

Area: T = 14.8439544915
Perimeter: p = 70.31992133488
Semiperimeter: s = 35.16596066744

Angle ∠ A = α = 138.571087149° = 138°34'15″ = 2.41985179549 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 1.42991285101° = 1°25'45″ = 0.02549429979 rad

Height: ha = 0.84879739951
Height: hb = 0.87329144068
Height: hc = 22.4987566339

Median: ma = 16.5111213218
Median: mb = 18.01102793407
Median: mc = 34.49773175629

Inradius: r = 0.42220623129
Circumradius: R = 26.44773050566

Vertex coordinates: A[1.31992133488; 0] B[0; 0] C[26.81215555092; 22.4987566339]
Centroid: CG[9.37769229527; 7.49991887797]
Coordinates of the circumscribed circle: U[0.66596066744; 26.43990783461]
Coordinates of the inscribed circle: I[1.16596066744; 0.42220623129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.42991285101° = 41°25'45″ = 2.41985179549 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 178.571087149° = 178°34'15″ = 0.02549429979 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 35 ; ; b = 34 ; ; beta = 40° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 34**2 = 35**2 + c**2 -2 * 34 * c * cos (40° ) ; ; ; ; c**2 -53.623c +69 =0 ; ; p=1; q=-53.6231110183; r=69 ; ; D = q**2 - 4pr = 53.623**2 - 4 * 1 * 69 = 2599.43803528 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 53.62 ± sqrt{ 2599.44 } }{ 2 } ; ; c_{1,2} = 26.8115555092 ± 25.4923421604 ; ; c_{1} = 52.3038976695 ; ;
c_{2} = 1.3192133488 ; ; ; ; (c -52.3038976695) (c -1.3192133488) = 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 = 35 ; ; b = 34 ; ; c = 1.32 ; ;

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

p = a+b+c = 35+34+1.32 = 70.32 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70.32 }{ 2 } = 35.16 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.16 * (35.16-35)(35.16-34)(35.16-1.32) } ; ; T = sqrt{ 220.21 } = 14.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.84 }{ 35 } = 0.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.84 }{ 34 } = 0.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.84 }{ 1.32 } = 22.5 ; ;

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{ 35**2-34**2-1.32**2 }{ 2 * 34 * 1.32 } ) = 138° 34'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 34**2-35**2-1.32**2 }{ 2 * 35 * 1.32 } ) = 40° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.32**2-35**2-34**2 }{ 2 * 34 * 35 } ) = 1° 25'45" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.84 }{ 35.16 } = 0.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 138° 34'15" } = 26.45 ; ;




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