Triangle calculator

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

You have entered side a, c and angle α.

Triangle has two solutions: a=38; b=25.57875251515; c=49 and a=38; b=37.41656605978; c=49.

#1 Obtuse scalene triangle.

Sides: a = 38   b = 25.57875251515   c = 49

Area: T = 480.0411264771
Perimeter: p = 112.5787525151
Semiperimeter: s = 56.28987625758

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 31.03988370467° = 31°2'20″ = 0.54217299025 rad
Angle ∠ C = γ = 98.96111629533° = 98°57'40″ = 1.72771981251 rad

Height: ha = 25.26553297248
Height: hb = 37.53661777128
Height: hc = 19.59435210111

Median: ma = 34.15655983177
Median: mb = 41.9439808676
Median: mc = 21.18661958935

Inradius: r = 8.52881900473
Circumradius: R = 24.80327384973

Vertex coordinates: A[49; 0] B[0; 0] C[32.55990837462; 19.59435210111]
Centroid: CG[27.18663612487; 6.53111736704]
Coordinates of the circumscribed circle: U[24.5; -3.86333970759]
Coordinates of the inscribed circle: I[30.71112374242; 8.52881900473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 148.9611162953° = 148°57'40″ = 0.54217299025 rad
∠ C' = γ' = 81.03988370467° = 81°2'20″ = 1.72771981251 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 = 38 ; ; b = 25.58 ; ; c = 49 ; ;

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

p = a+b+c = 38+25.58+49 = 112.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112.58 }{ 2 } = 56.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56.29 * (56.29-38)(56.29-25.58)(56.29-49) } ; ; T = sqrt{ 230439.62 } = 480.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 480.04 }{ 38 } = 25.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 480.04 }{ 25.58 } = 37.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 480.04 }{ 49 } = 19.59 ; ;

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{ 38**2-25.58**2-49**2 }{ 2 * 25.58 * 49 } ) = 50° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25.58**2-38**2-49**2 }{ 2 * 38 * 49 } ) = 31° 2'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 49**2-38**2-25.58**2 }{ 2 * 25.58 * 38 } ) = 98° 57'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 480.04 }{ 56.29 } = 8.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38 }{ 2 * sin 50° } = 24.8 ; ;





#2 Acute scalene triangle.

Sides: a = 38   b = 37.41656605978   c = 49

Area: T = 702.222044272
Perimeter: p = 124.4165660598
Semiperimeter: s = 62.20878302989

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 48.96111629533° = 48°57'40″ = 0.85545334991 rad
Angle ∠ C = γ = 81.03988370467° = 81°2'20″ = 1.41443945285 rad

Height: ha = 36.95989706695
Height: hb = 37.53661777128
Height: hc = 28.66220588865

Median: ma = 39.23660271814
Median: mb = 39.65549755454
Median: mc = 28.66655861441

Inradius: r = 11.28882966557
Circumradius: R = 24.80327384973

Vertex coordinates: A[49; 0] B[0; 0] C[24.95496769595; 28.66220588865]
Centroid: CG[24.65498923198; 9.55440196288]
Coordinates of the circumscribed circle: U[24.5; 3.86333970759]
Coordinates of the inscribed circle: I[24.79221697011; 11.28882966557]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 131.0398837047° = 131°2'20″ = 0.85545334991 rad
∠ C' = γ' = 98.96111629533° = 98°57'40″ = 1.41443945285 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 = 38 ; ; b = 37.42 ; ; c = 49 ; ;

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

p = a+b+c = 38+37.42+49 = 124.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.42 }{ 2 } = 62.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.21 * (62.21-38)(62.21-37.42)(62.21-49) } ; ; T = sqrt{ 493113.55 } = 702.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 702.22 }{ 38 } = 36.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 702.22 }{ 37.42 } = 37.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 702.22 }{ 49 } = 28.66 ; ;

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{ 38**2-37.42**2-49**2 }{ 2 * 37.42 * 49 } ) = 50° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 37.42**2-38**2-49**2 }{ 2 * 38 * 49 } ) = 48° 57'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 49**2-38**2-37.42**2 }{ 2 * 37.42 * 38 } ) = 81° 2'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 702.22 }{ 62.21 } = 11.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38 }{ 2 * sin 50° } = 24.8 ; ; : Nr. 1




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