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?

1. Input data entered: side a, b and area T.

a = 350 ; ; b = 227 ; ; T = 29185 ; ;

2. From area T and side a we calculate h_a - The area of the triangle is the product of the length of the base and the height divided by two:

T = fraction{ a h_a }{ 2 } ; ; ; ; h_a = fraction{ 2 T }{ a } = fraction{ 2 * 29185 }{ 350 } = 166.771 ; ;


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 ; ;

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

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

4. Semiperimeter of the triangle

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

5. 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 ; ;

6. 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 ; ;

7. 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" ; ;

8. Inradius

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

9. 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?

1. Input data entered: side a, b and area T.

a = 350 ; ; b = 227 ; ; T = 29185 ; ; : Nr. 1

2. From area T and side a we calculate h_a - The area of the triangle is the product of the length of the base and the height divided by two:

T = fraction{ a h_a }{ 2 } ; ; ; ; h_a = fraction{ 2 T }{ a } = fraction{ 2 * 29185 }{ 350 } = 166.771 ; ; : Nr. 1


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 ; ;

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

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

4. Semiperimeter of the triangle

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

5. 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 ; ;

6. 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 ; ;

7. 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" ; ;

8. Inradius

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

9. Circumradius

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




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