Triangle calculator

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

You have entered side a, b and angle β.

Triangle has two solutions: a=39.2; b=28.6; c=14.04110700862 and a=39.2; b=28.6; c=51.18441330889.

#1 Obtuse scalene triangle.

Sides: a = 39.2   b = 28.6   c = 14.04110700862

Area: T = 152.6965946057
Perimeter: p = 81.84110700862
Semiperimeter: s = 40.92105350431

Angle ∠ A = α = 130.493293264° = 130°29'35″ = 2.27875313251 rad
Angle ∠ B = β = 33.7° = 33°42' = 0.58881759579 rad
Angle ∠ C = γ = 15.80770673602° = 15°48'25″ = 0.27658853705 rad

Height: ha = 7.79106094927
Height: hb = 10.67880381858
Height: hc = 21.7549901556

Median: ma = 11.1088367323
Median: mb = 25.73772458624
Median: mc = 33.58658912002

Inradius: r = 3.73215236933
Circumradius: R = 25.7732990216

Vertex coordinates: A[14.04110700862; 0] B[0; 0] C[32.61326015875; 21.7549901556]
Centroid: CG[15.55112238912; 7.25499671853]
Coordinates of the circumscribed circle: U[7.02105350431; 24.79883691476]
Coordinates of the inscribed circle: I[12.32105350431; 3.73215236933]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 49.50770673602° = 49°30'25″ = 2.27875313251 rad
∠ B' = β' = 146.3° = 146°18' = 0.58881759579 rad
∠ C' = γ' = 164.193293264° = 164°11'35″ = 0.27658853705 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 = 39.2 ; ; b = 28.6 ; ; c = 14.04 ; ;

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

p = a+b+c = 39.2+28.6+14.04 = 81.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81.84 }{ 2 } = 40.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.92 * (40.92-39.2)(40.92-28.6)(40.92-14.04) } ; ; T = sqrt{ 23316.05 } = 152.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 152.7 }{ 39.2 } = 7.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 152.7 }{ 28.6 } = 10.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 152.7 }{ 14.04 } = 21.75 ; ;

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{ 39.2**2-28.6**2-14.04**2 }{ 2 * 28.6 * 14.04 } ) = 130° 29'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28.6**2-39.2**2-14.04**2 }{ 2 * 39.2 * 14.04 } ) = 33° 42' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.04**2-39.2**2-28.6**2 }{ 2 * 28.6 * 39.2 } ) = 15° 48'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 152.7 }{ 40.92 } = 3.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39.2 }{ 2 * sin 130° 29'35" } = 25.77 ; ;





#2 Obtuse scalene triangle.

Sides: a = 39.2   b = 28.6   c = 51.18441330889

Area: T = 556.6254927955
Perimeter: p = 118.9844133089
Semiperimeter: s = 59.49220665444

Angle ∠ A = α = 49.50770673602° = 49°30'25″ = 0.86440613284 rad
Angle ∠ B = β = 33.7° = 33°42' = 0.58881759579 rad
Angle ∠ C = γ = 96.79329326398° = 96°47'35″ = 1.68993553672 rad

Height: ha = 28.39992310181
Height: hb = 38.92548201367
Height: hc = 21.7549901556

Median: ma = 36.53439258776
Median: mb = 43.28766924127
Median: mc = 22.85548929113

Inradius: r = 9.35662883303
Circumradius: R = 25.7732990216

Vertex coordinates: A[51.18441330889; 0] B[0; 0] C[32.61326015875; 21.7549901556]
Centroid: CG[27.93222448921; 7.25499671853]
Coordinates of the circumscribed circle: U[25.59220665444; -3.04884675916]
Coordinates of the inscribed circle: I[30.89220665444; 9.35662883303]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.493293264° = 130°29'35″ = 0.86440613284 rad
∠ B' = β' = 146.3° = 146°18' = 0.58881759579 rad
∠ C' = γ' = 83.20770673602° = 83°12'25″ = 1.68993553672 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 = 39.2 ; ; b = 28.6 ; ; c = 51.18 ; ;

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

p = a+b+c = 39.2+28.6+51.18 = 118.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.98 }{ 2 } = 59.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.49 * (59.49-39.2)(59.49-28.6)(59.49-51.18) } ; ; T = sqrt{ 309831.31 } = 556.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 556.62 }{ 39.2 } = 28.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 556.62 }{ 28.6 } = 38.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 556.62 }{ 51.18 } = 21.75 ; ;

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{ 39.2**2-28.6**2-51.18**2 }{ 2 * 28.6 * 51.18 } ) = 49° 30'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28.6**2-39.2**2-51.18**2 }{ 2 * 39.2 * 51.18 } ) = 33° 42' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 51.18**2-39.2**2-28.6**2 }{ 2 * 28.6 * 39.2 } ) = 96° 47'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 556.62 }{ 59.49 } = 9.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39.2 }{ 2 * sin 49° 30'25" } = 25.77 ; ;




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