Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=3.92223491461; b=49; c=48 and a=24.73300779167; b=49; c=48.

#1 Obtuse scalene triangle.

Sides: a = 3.92223491461   b = 49   c = 48

Area: T = 91.8998548003
Perimeter: p = 100.9222349146
Semiperimeter: s = 50.46111745731

Angle ∠ A = α = 4.48219495841° = 4°28'55″ = 0.07882247772 rad
Angle ∠ B = β = 102.5188050416° = 102°31'5″ = 1.78992775225 rad
Angle ∠ C = γ = 73° = 1.2744090354 rad

Height: ha = 46.85989330422
Height: hb = 3.7510961143
Height: hc = 3.82991061668

Median: ma = 48.46329115334
Median: mb = 23.65325349891
Median: mc = 25.14334367462

Inradius: r = 1.82111733829
Circumradius: R = 25.09766021557

Vertex coordinates: A[48; 0] B[0; 0] C[-0.85501580956; 3.82991061668]
Centroid: CG[15.71766139681; 1.27663687223]
Coordinates of the circumscribed circle: U[24; 7.3387536355]
Coordinates of the inscribed circle: I[1.46111745731; 1.82111733829]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5188050416° = 175°31'5″ = 0.07882247772 rad
∠ B' = β' = 77.48219495841° = 77°28'55″ = 1.78992775225 rad
∠ C' = γ' = 107° = 1.2744090354 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 = 3.92 ; ; b = 49 ; ; c = 48 ; ;

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

p = a+b+c = 3.92+49+48 = 100.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 100.92 }{ 2 } = 50.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.46 * (50.46-3.92)(50.46-49)(50.46-48) } ; ; T = sqrt{ 8445.34 } = 91.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.9 }{ 3.92 } = 46.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.9 }{ 49 } = 3.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.9 }{ 48 } = 3.83 ; ;

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{ 3.92**2-49**2-48**2 }{ 2 * 49 * 48 } ) = 4° 28'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-3.92**2-48**2 }{ 2 * 3.92 * 48 } ) = 102° 31'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 48**2-3.92**2-49**2 }{ 2 * 49 * 3.92 } ) = 73° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.9 }{ 50.46 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.92 }{ 2 * sin 4° 28'55" } = 25.1 ; ;





#2 Acute scalene triangle.

Sides: a = 24.73300779167   b = 49   c = 48

Area: T = 579.4132532614
Perimeter: p = 121.7330077917
Semiperimeter: s = 60.86550389584

Angle ∠ A = α = 29.51880504159° = 29°31'5″ = 0.51551871685 rad
Angle ∠ B = β = 77.48219495841° = 77°28'55″ = 1.35223151311 rad
Angle ∠ C = γ = 73° = 1.2744090354 rad

Height: ha = 46.85989330422
Height: hb = 23.64994911271
Height: hc = 24.14221888589

Median: ma = 46.98999553471
Median: mb = 29.28437561949
Median: mc = 30.50106291227

Inradius: r = 9.52196280579
Circumradius: R = 25.09766021557

Vertex coordinates: A[48; 0] B[0; 0] C[5.36601745184; 24.14221888589]
Centroid: CG[17.78767248395; 8.04773962863]
Coordinates of the circumscribed circle: U[24; 7.3387536355]
Coordinates of the inscribed circle: I[11.86550389584; 9.52196280579]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4821949584° = 150°28'55″ = 0.51551871685 rad
∠ B' = β' = 102.5188050416° = 102°31'5″ = 1.35223151311 rad
∠ C' = γ' = 107° = 1.2744090354 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 = 24.73 ; ; b = 49 ; ; c = 48 ; ;

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

p = a+b+c = 24.73+49+48 = 121.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 121.73 }{ 2 } = 60.87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.87 * (60.87-24.73)(60.87-49)(60.87-48) } ; ; T = sqrt{ 335718.88 } = 579.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 579.41 }{ 24.73 } = 46.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 579.41 }{ 49 } = 23.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 579.41 }{ 48 } = 24.14 ; ;

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{ 24.73**2-49**2-48**2 }{ 2 * 49 * 48 } ) = 29° 31'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-24.73**2-48**2 }{ 2 * 24.73 * 48 } ) = 77° 28'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 48**2-24.73**2-49**2 }{ 2 * 49 * 24.73 } ) = 73° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 579.41 }{ 60.87 } = 9.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.73 }{ 2 * sin 29° 31'5" } = 25.1 ; ;




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