Triangle calculator

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

You have entered side a, c and height hc.

Triangle has two solutions: a=405; b=1382.678781137; c=982 and a=405; b=587.2821933953; c=982.

#1 Obtuse scalene triangle.

Sides: a = 405   b = 1382.678781137   c = 982

Area: T = 34370
Perimeter: p = 2769.678781137
Semiperimeter: s = 1384.839890568

Angle ∠ A = α = 2.90219195744° = 2°54'7″ = 0.05106480512 rad
Angle ∠ B = β = 170.0477044832° = 170°2'49″ = 2.96878808156 rad
Angle ∠ C = γ = 7.05110355939° = 7°3'4″ = 0.12330637868 rad

Height: ha = 169.7288395062
Height: hb = 49.71551248359
Height: hc = 70

Median: ma = 1181.971069127
Median: mb = 293.6410966977
Median: mc = 892.6543608644

Inradius: r = 24.81987712368
Circumradius: R = 3999.889938289

Vertex coordinates: A[982; 0] B[0; 0] C[-398.9054750536; 70]
Centroid: CG[194.3655083155; 23.33333333333]
Coordinates of the circumscribed circle: U[491; 3969.63990359]
Coordinates of the inscribed circle: I[2.16110943155; 24.81987712368]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.0988080426° = 177°5'53″ = 0.05106480512 rad
∠ B' = β' = 9.95329551683° = 9°57'11″ = 2.96878808156 rad
∠ C' = γ' = 172.9498964406° = 172°56'56″ = 0.12330637868 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 = 405 ; ; b = 1382.68 ; ; c = 982 ; ;

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

p = a+b+c = 405+1382.68+982 = 2769.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2769.68 }{ 2 } = 1384.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1384.84 * (1384.84-405)(1384.84-1382.68)(1384.84-982) } ; ; T = sqrt{ 1181296900 } = 34370 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34370 }{ 405 } = 169.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34370 }{ 1382.68 } = 49.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34370 }{ 982 } = 70 ; ;

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{ 405**2-1382.68**2-982**2 }{ 2 * 1382.68 * 982 } ) = 2° 54'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1382.68**2-405**2-982**2 }{ 2 * 405 * 982 } ) = 170° 2'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 982**2-405**2-1382.68**2 }{ 2 * 1382.68 * 405 } ) = 7° 3'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34370 }{ 1384.84 } = 24.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 405 }{ 2 * sin 2° 54'7" } = 3999.89 ; ;





#2 Obtuse scalene triangle.

Sides: a = 405   b = 587.2821933953   c = 982

Area: T = 34370
Perimeter: p = 1974.282193395
Semiperimeter: s = 987.1410966977

Angle ∠ A = α = 6.84655408805° = 6°50'44″ = 0.11994772274 rad
Angle ∠ B = β = 9.95329551683° = 9°57'11″ = 0.1743711838 rad
Angle ∠ C = γ = 163.2021503951° = 163°12'5″ = 2.84884035882 rad

Height: ha = 169.7288395062
Height: hb = 117.0487700646
Height: hc = 70

Median: ma = 783.3329933664
Median: mb = 691.3398905684
Median: mc = 115.6798584768

Inradius: r = 34.81877222401
Circumradius: R = 1698.923273751

Vertex coordinates: A[982; 0] B[0; 0] C[398.9054750536; 70]
Centroid: CG[460.3021583512; 23.33333333333]
Coordinates of the circumscribed circle: U[491; -1626.425475019]
Coordinates of the inscribed circle: I[399.8599033023; 34.81877222401]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.1544459119° = 173°9'16″ = 0.11994772274 rad
∠ B' = β' = 170.0477044832° = 170°2'49″ = 0.1743711838 rad
∠ C' = γ' = 16.79884960488° = 16°47'55″ = 2.84884035882 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 = 405 ; ; b = 587.28 ; ; c = 982 ; ;

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

p = a+b+c = 405+587.28+982 = 1974.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1974.28 }{ 2 } = 987.14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 987.14 * (987.14-405)(987.14-587.28)(987.14-982) } ; ; T = sqrt{ 1181296900 } = 34370 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34370 }{ 405 } = 169.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34370 }{ 587.28 } = 117.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34370 }{ 982 } = 70 ; ;

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{ 405**2-587.28**2-982**2 }{ 2 * 587.28 * 982 } ) = 6° 50'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 587.28**2-405**2-982**2 }{ 2 * 405 * 982 } ) = 9° 57'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 982**2-405**2-587.28**2 }{ 2 * 587.28 * 405 } ) = 163° 12'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34370 }{ 987.14 } = 34.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 405 }{ 2 * sin 6° 50'44" } = 1698.92 ; ;




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