Triangle calculator

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

You have entered side a, c and angle γ.

Triangle has two solutions: a=18.7; b=3.31112488771; c=16.1 and a=18.7; b=27.32550375794; c=16.1.

#1 Obtuse scalene triangle.

Sides: a = 18.7   b = 3.31112488771   c = 16.1

Area: T = 17.75880279927
Perimeter: p = 38.11112488771
Semiperimeter: s = 19.05656244385

Angle ∠ A = α = 138.2255264641° = 138°13'31″ = 2.41224859774 rad
Angle ∠ B = β = 6.77547353587° = 6°46'29″ = 0.1188241438 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 1.89992543308
Height: hb = 10.72658793598
Height: hc = 2.20659662103

Median: ma = 6.90439615123
Median: mb = 17.37697699386
Median: mc = 10.74882409985

Inradius: r = 0.93219048058
Circumradius: R = 14.03547467047

Vertex coordinates: A[16.1; 0] B[0; 0] C[18.56994295303; 2.20659662103]
Centroid: CG[11.55664765101; 0.73553220701]
Coordinates of the circumscribed circle: U[8.05; 11.49765914543]
Coordinates of the inscribed circle: I[15.74443755615; 0.93219048058]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.77547353587° = 41°46'29″ = 2.41224859774 rad
∠ B' = β' = 173.2255264641° = 173°13'31″ = 0.1188241438 rad
∠ C' = γ' = 145° = 0.61108652382 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 = 18.7 ; ; b = 3.31 ; ; c = 16.1 ; ;

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

p = a+b+c = 18.7+3.31+16.1 = 38.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38.11 }{ 2 } = 19.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.06 * (19.06-18.7)(19.06-3.31)(19.06-16.1) } ; ; T = sqrt{ 315.35 } = 17.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.76 }{ 18.7 } = 1.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.76 }{ 3.31 } = 10.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.76 }{ 16.1 } = 2.21 ; ;

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{ 18.7**2-3.31**2-16.1**2 }{ 2 * 3.31 * 16.1 } ) = 138° 13'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.31**2-18.7**2-16.1**2 }{ 2 * 18.7 * 16.1 } ) = 6° 46'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16.1**2-18.7**2-3.31**2 }{ 2 * 3.31 * 18.7 } ) = 35° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.76 }{ 19.06 } = 0.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.7 }{ 2 * sin 138° 13'31" } = 14.03 ; ;





#2 Obtuse scalene triangle.

Sides: a = 18.7   b = 27.32550375794   c = 16.1

Area: T = 146.5432528289
Perimeter: p = 62.12550375794
Semiperimeter: s = 31.06325187897

Angle ∠ A = α = 41.77547353587° = 41°46'29″ = 0.72991066762 rad
Angle ∠ B = β = 103.2255264641° = 103°13'31″ = 1.80216207392 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 15.67329976779
Height: hb = 10.72658793598
Height: hc = 18.20440407812

Median: ma = 20.38440952548
Median: mb = 10.8532906538
Median: mc = 21.98657076156

Inradius: r = 4.7187664053
Circumradius: R = 14.03547467047

Vertex coordinates: A[16.1; 0] B[0; 0] C[-4.27881887799; 18.20440407812]
Centroid: CG[3.941060374; 6.06880135937]
Coordinates of the circumscribed circle: U[8.05; 11.49765914543]
Coordinates of the inscribed circle: I[3.73774812103; 4.7187664053]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2255264641° = 138°13'31″ = 0.72991066762 rad
∠ B' = β' = 76.77547353587° = 76°46'29″ = 1.80216207392 rad
∠ C' = γ' = 145° = 0.61108652382 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 = 18.7 ; ; b = 27.33 ; ; c = 16.1 ; ;

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

p = a+b+c = 18.7+27.33+16.1 = 62.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62.13 }{ 2 } = 31.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.06 * (31.06-18.7)(31.06-27.33)(31.06-16.1) } ; ; T = sqrt{ 21474.71 } = 146.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.54 }{ 18.7 } = 15.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.54 }{ 27.33 } = 10.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.54 }{ 16.1 } = 18.2 ; ;

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{ 18.7**2-27.33**2-16.1**2 }{ 2 * 27.33 * 16.1 } ) = 41° 46'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27.33**2-18.7**2-16.1**2 }{ 2 * 18.7 * 16.1 } ) = 103° 13'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16.1**2-18.7**2-27.33**2 }{ 2 * 27.33 * 18.7 } ) = 35° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.54 }{ 31.06 } = 4.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.7 }{ 2 * sin 41° 46'29" } = 14.03 ; ;




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