Triangle calculator

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

You have entered side a, b and angle α.

Triangle has two solutions: a=11.2; b=13.4; c=2.45771059396 and a=11.2; b=13.4; c=22.02659123252.

#1 Obtuse scalene triangle.

Sides: a = 11.2   b = 13.4   c = 2.45771059396

Area: T = 6.69659466445
Perimeter: p = 27.05771059396
Semiperimeter: s = 13.52985529698

Angle ∠ A = α = 24° = 0.41988790205 rad
Angle ∠ B = β = 150.8810591188° = 150°52'50″ = 2.63333630936 rad
Angle ∠ C = γ = 5.11994088121° = 5°7'10″ = 0.08993505395 rad

Height: ha = 1.19657047579
Height: hb = 0.99993950216
Height: hc = 5.45502710172

Median: ma = 7.83882832814
Median: mb = 4.5666036005
Median: mc = 12.28878255847

Inradius: r = 0.49549492129
Circumradius: R = 13.76881226792

Vertex coordinates: A[2.45771059396; 0] B[0; 0] C[-9.78444031928; 5.45502710172]
Centroid: CG[-2.44224324177; 1.81767570057]
Coordinates of the circumscribed circle: U[1.22985529698; 13.71332001995]
Coordinates of the inscribed circle: I[0.12985529698; 0.49549492129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156° = 0.41988790205 rad
∠ B' = β' = 29.11994088121° = 29°7'10″ = 2.63333630936 rad
∠ C' = γ' = 174.8810591188° = 174°52'50″ = 0.08993505395 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 = 11.2 ; ; b = 13.4 ; ; c = 2.46 ; ;

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

p = a+b+c = 11.2+13.4+2.46 = 27.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.06 }{ 2 } = 13.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.53 * (13.53-11.2)(13.53-13.4)(13.53-2.46) } ; ; T = sqrt{ 44.84 } = 6.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.7 }{ 11.2 } = 1.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.7 }{ 13.4 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.7 }{ 2.46 } = 5.45 ; ;

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{ 11.2**2-13.4**2-2.46**2 }{ 2 * 13.4 * 2.46 } ) = 24° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.4**2-11.2**2-2.46**2 }{ 2 * 11.2 * 2.46 } ) = 150° 52'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.46**2-11.2**2-13.4**2 }{ 2 * 13.4 * 11.2 } ) = 5° 7'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.7 }{ 13.53 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.2 }{ 2 * sin 24° } = 13.77 ; ;





#2 Obtuse scalene triangle.

Sides: a = 11.2   b = 13.4   c = 22.02659123252

Area: T = 60.02435957869
Perimeter: p = 46.62659123252
Semiperimeter: s = 23.31329561626

Angle ∠ A = α = 24° = 0.41988790205 rad
Angle ∠ B = β = 29.11994088121° = 29°7'10″ = 0.508822956 rad
Angle ∠ C = γ = 126.8810591188° = 126°52'50″ = 2.21444840731 rad

Height: ha = 10.71884992477
Height: hb = 8.95987456398
Height: hc = 5.45502710172

Median: ma = 17.34990751015
Median: mb = 16.13769268102
Median: mc = 5.58770203652

Inradius: r = 2.57546883136
Circumradius: R = 13.76881226792

Vertex coordinates: A[22.02659123252; 0] B[0; 0] C[9.78444031928; 5.45502710172]
Centroid: CG[10.6033438506; 1.81767570057]
Coordinates of the circumscribed circle: U[11.01329561626; -8.26329291822]
Coordinates of the inscribed circle: I[9.91329561626; 2.57546883136]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156° = 0.41988790205 rad
∠ B' = β' = 150.8810591188° = 150°52'50″ = 0.508822956 rad
∠ C' = γ' = 53.11994088121° = 53°7'10″ = 2.21444840731 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 = 11.2 ; ; b = 13.4 ; ; c = 22.03 ; ;

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

p = a+b+c = 11.2+13.4+22.03 = 46.63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46.63 }{ 2 } = 23.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.31 * (23.31-11.2)(23.31-13.4)(23.31-22.03) } ; ; T = sqrt{ 3602.83 } = 60.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60.02 }{ 11.2 } = 10.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60.02 }{ 13.4 } = 8.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60.02 }{ 22.03 } = 5.45 ; ;

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{ 11.2**2-13.4**2-22.03**2 }{ 2 * 13.4 * 22.03 } ) = 24° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.4**2-11.2**2-22.03**2 }{ 2 * 11.2 * 22.03 } ) = 29° 7'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22.03**2-11.2**2-13.4**2 }{ 2 * 13.4 * 11.2 } ) = 126° 52'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60.02 }{ 23.31 } = 2.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.2 }{ 2 * sin 24° } = 13.77 ; ; : Nr. 1




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

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