Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and area T.

Triangle has two solutions: a=350; b=227; c=530.8766313731 and a=350; b=227; c=257.3498673048.

#1 Obtuse scalene triangle.

Sides: a = 350   b = 227   c = 530.8766313731

Area: T = 29185
Perimeter: p = 1107.876631373
Semiperimeter: s = 553.9388156865

Angle ∠ A = α = 28.97107117801° = 28°58'15″ = 0.50656343072 rad
Angle ∠ B = β = 18.30991251195° = 18°18'33″ = 0.32195545165 rad
Angle ∠ C = γ = 132.72201631° = 132°43'13″ = 2.31664038299 rad

Height: ha = 166.7711428571
Height: hb = 257.1376563877
Height: hc = 109.9550281243

Median: ma = 368.8555432711
Median: mb = 435.066617915
Median: mc = 128.6744336524

Inradius: r = 52.68663868074
Circumradius: R = 361.3299667003

Vertex coordinates: A[530.8766313731; 0] B[0; 0] C[332.2811410336; 109.9550281243]
Centroid: CG[287.7199241355; 36.65500937477]
Coordinates of the circumscribed circle: U[265.4388156865; -245.1122289076]
Coordinates of the inscribed circle: I[326.9388156865; 52.68663868074]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.029928822° = 151°1'45″ = 0.50656343072 rad
∠ B' = β' = 161.6910874881° = 161°41'27″ = 0.32195545165 rad
∠ C' = γ' = 47.28798368996° = 47°16'47″ = 2.31664038299 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 = 350 ; ; b = 227 ; ; c = 530.88 ; ;

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

p = a+b+c = 350+227+530.88 = 1107.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1107.88 }{ 2 } = 553.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 553.94 * (553.94-350)(553.94-227)(553.94-530.88) } ; ; T = sqrt{ 851764225 } = 29185 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29185 }{ 350 } = 166.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29185 }{ 227 } = 257.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29185 }{ 530.88 } = 109.95 ; ;

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{ 350**2-227**2-530.88**2 }{ 2 * 227 * 530.88 } ) = 28° 58'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 227**2-350**2-530.88**2 }{ 2 * 350 * 530.88 } ) = 18° 18'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 530.88**2-350**2-227**2 }{ 2 * 227 * 350 } ) = 132° 43'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29185 }{ 553.94 } = 52.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 350 }{ 2 * sin 28° 58'15" } = 361.3 ; ;





#2 Obtuse scalene triangle.

Sides: a = 350   b = 227   c = 257.3498673048

Area: T = 29185
Perimeter: p = 834.3498673048
Semiperimeter: s = 417.1744336524

Angle ∠ A = α = 92.32664098129° = 92°19'35″ = 1.61113998378 rad
Angle ∠ B = β = 40.39437532875° = 40°23'37″ = 0.70550039921 rad
Angle ∠ C = γ = 47.28798368996° = 47°16'47″ = 0.82551888237 rad

Height: ha = 166.7711428571
Height: hb = 257.1376563877
Height: hc = 226.8132904487

Median: ma = 168.0888279662
Median: mb = 285.4550380557
Median: mc = 265.4388156865

Inradius: r = 69.9598761709
Circumradius: R = 175.1444355608

Vertex coordinates: A[257.3498673048; 0] B[0; 0] C[266.5633137658; 226.8132904487]
Centroid: CG[174.6377270235; 75.60443014958]
Coordinates of the circumscribed circle: U[128.6744336524; 118.8211127841]
Coordinates of the inscribed circle: I[190.1744336524; 69.9598761709]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 87.67435901871° = 87°40'25″ = 1.61113998378 rad
∠ B' = β' = 139.6066246713° = 139°36'22″ = 0.70550039921 rad
∠ C' = γ' = 132.72201631° = 132°43'13″ = 0.82551888237 rad

Calculate another triangle

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 = 350 ; ; b = 227 ; ; c = 257.35 ; ;

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

p = a+b+c = 350+227+257.35 = 834.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 834.35 }{ 2 } = 417.17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 417.17 * (417.17-350)(417.17-227)(417.17-257.35) } ; ; T = sqrt{ 851764225 } = 29185 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29185 }{ 350 } = 166.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29185 }{ 227 } = 257.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29185 }{ 257.35 } = 226.81 ; ;

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{ 350**2-227**2-257.35**2 }{ 2 * 227 * 257.35 } ) = 92° 19'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 227**2-350**2-257.35**2 }{ 2 * 350 * 257.35 } ) = 40° 23'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 257.35**2-350**2-227**2 }{ 2 * 227 * 350 } ) = 47° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29185 }{ 417.17 } = 69.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 350 }{ 2 * sin 92° 19'35" } = 175.14 ; ;




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