Triangle calculator

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

You have entered side b, c and angle β.

Triangle has two solutions: a=7.9099114914; b=33; c=38 and a=44.88549212409; b=33; c=38.

#1 Obtuse scalene triangle.

Sides: a = 7.9099114914   b = 33   c = 38

Area: T = 108.0977481719
Perimeter: p = 78.9099114914
Semiperimeter: s = 39.4554557457

Angle ∠ A = α = 9.92876383247° = 9°55'40″ = 0.17332699757 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 124.0722361675° = 124°4'20″ = 2.1655471222 rad

Height: ha = 27.33549124129
Height: hb = 6.55113625284
Height: hc = 5.68993411431

Median: ma = 35.36875200618
Median: mb = 21.93223288632
Median: mc = 14.6555273773

Inradius: r = 2.74397970903
Circumradius: R = 22.93876992518

Vertex coordinates: A[38; 0] B[0; 0] C[5.49441328779; 5.68993411431]
Centroid: CG[14.49880442926; 1.89664470477]
Coordinates of the circumscribed circle: U[19; -12.8510604926]
Coordinates of the inscribed circle: I[6.4554557457; 2.74397970903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0722361675° = 170°4'20″ = 0.17332699757 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 55.92876383247° = 55°55'40″ = 2.1655471222 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 = 7.91 ; ; b = 33 ; ; c = 38 ; ;

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

p = a+b+c = 7.91+33+38 = 78.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78.91 }{ 2 } = 39.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.45 * (39.45-7.91)(39.45-33)(39.45-38) } ; ; T = sqrt{ 11685.07 } = 108.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 108.1 }{ 7.91 } = 27.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 108.1 }{ 33 } = 6.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 108.1 }{ 38 } = 5.69 ; ;

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{ 7.91**2-33**2-38**2 }{ 2 * 33 * 38 } ) = 9° 55'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33**2-7.91**2-38**2 }{ 2 * 7.91 * 38 } ) = 46° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 38**2-7.91**2-33**2 }{ 2 * 33 * 7.91 } ) = 124° 4'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 108.1 }{ 39.45 } = 2.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.91 }{ 2 * sin 9° 55'40" } = 22.94 ; ;





#2 Acute scalene triangle.

Sides: a = 44.88549212409   b = 33   c = 38

Area: T = 613.4632695389
Perimeter: p = 115.8854921241
Semiperimeter: s = 57.94224606204

Angle ∠ A = α = 78.07223616753° = 78°4'20″ = 1.3632619766 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 55.92876383247° = 55°55'40″ = 0.97661214316 rad

Height: ha = 27.33549124129
Height: hb = 37.18795572963
Height: hc = 32.28875102836

Median: ma = 27.61994851744
Median: mb = 38.17216920951
Median: mc = 34.50883769163

Inradius: r = 10.58774463877
Circumradius: R = 22.93876992518

Vertex coordinates: A[38; 0] B[0; 0] C[31.18796862474; 32.28875102836]
Centroid: CG[23.06598954158; 10.76325034279]
Coordinates of the circumscribed circle: U[19; 12.8510604926]
Coordinates of the inscribed circle: I[24.94224606204; 10.58774463877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.9287638325° = 101°55'40″ = 1.3632619766 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 124.0722361675° = 124°4'20″ = 0.97661214316 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 = 44.88 ; ; b = 33 ; ; c = 38 ; ;

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

p = a+b+c = 44.88+33+38 = 115.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 115.88 }{ 2 } = 57.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.94 * (57.94-44.88)(57.94-33)(57.94-38) } ; ; T = sqrt{ 376336.48 } = 613.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 613.46 }{ 44.88 } = 27.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 613.46 }{ 33 } = 37.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 613.46 }{ 38 } = 32.29 ; ;

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{ 44.88**2-33**2-38**2 }{ 2 * 33 * 38 } ) = 78° 4'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33**2-44.88**2-38**2 }{ 2 * 44.88 * 38 } ) = 46° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 38**2-44.88**2-33**2 }{ 2 * 33 * 44.88 } ) = 55° 55'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 613.46 }{ 57.94 } = 10.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 44.88 }{ 2 * sin 78° 4'20" } = 22.94 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.