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=441.59; b=125.9155131498; c=378.38 and a=441.59; b=411.6298873222; c=378.38.

#1 Obtuse scalene triangle.

Sides: a = 441.59   b = 125.9155131498   c = 378.38

Area: T = 22058.82198297
Perimeter: p = 945.8855131498
Semiperimeter: s = 472.9432565749

Angle ∠ A = α = 112.1821924892° = 112°10'55″ = 1.95879439506 rad
Angle ∠ B = β = 15.31097418076° = 15°18'35″ = 0.26772054022 rad
Angle ∠ C = γ = 52.50883333° = 52°30'30″ = 0.91664433008 rad

Height: ha = 99.90663376873
Height: hb = 350.3765996392
Height: hc = 116.5966119402

Median: ma = 175.3932674719
Median: mb = 406.3533197557
Median: mc = 263.885504717

Inradius: r = 46.64216462108
Circumradius: R = 238.4422167729

Vertex coordinates: A[378.38; 0] B[0; 0] C[425.9199092129; 116.5966119402]
Centroid: CG[268.1099697376; 38.8655373134]
Coordinates of the circumscribed circle: U[189.19; 145.1276879838]
Coordinates of the inscribed circle: I[347.0277434251; 46.64216462108]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.81880751076° = 67°49'5″ = 1.95879439506 rad
∠ B' = β' = 164.6990258192° = 164°41'25″ = 0.26772054022 rad
∠ C' = γ' = 127.49216667° = 127°29'30″ = 0.91664433008 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 = 441.59 ; ; b = 125.92 ; ; c = 378.38 ; ;

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

p = a+b+c = 441.59+125.92+378.38 = 945.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 945.89 }{ 2 } = 472.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 472.94 * (472.94-441.59)(472.94-125.92)(472.94-378.38) } ; ; T = sqrt{ 486591532.28 } = 22058.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22058.82 }{ 441.59 } = 99.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22058.82 }{ 125.92 } = 350.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22058.82 }{ 378.38 } = 116.6 ; ;

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{ 441.59**2-125.92**2-378.38**2 }{ 2 * 125.92 * 378.38 } ) = 112° 10'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 125.92**2-441.59**2-378.38**2 }{ 2 * 441.59 * 378.38 } ) = 15° 18'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 378.38**2-441.59**2-125.92**2 }{ 2 * 125.92 * 441.59 } ) = 52° 30'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22058.82 }{ 472.94 } = 46.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 441.59 }{ 2 * sin 112° 10'55" } = 238.44 ; ;





#2 Acute scalene triangle.

Sides: a = 441.59   b = 411.6298873222   c = 378.38

Area: T = 72112.43882994
Perimeter: p = 1231.599887322
Semiperimeter: s = 615.7999436611

Angle ∠ A = α = 67.81880751076° = 67°49'5″ = 1.1843648703 rad
Angle ∠ B = β = 59.67435915924° = 59°40'25″ = 1.04215006498 rad
Angle ∠ C = γ = 52.50883333° = 52°30'30″ = 0.91664433008 rad

Height: ha = 326.6043583865
Height: hb = 350.3765996392
Height: hc = 381.1644111736

Median: ma = 327.9554943262
Median: mb = 355.9877350804
Median: mc = 382.6588036091

Inradius: r = 117.1043774398
Circumradius: R = 238.4422167729

Vertex coordinates: A[378.38; 0] B[0; 0] C[222.9770060825; 381.1644111736]
Centroid: CG[200.4550020275; 127.0554703912]
Coordinates of the circumscribed circle: U[189.19; 145.1276879838]
Coordinates of the inscribed circle: I[204.1710563389; 117.1043774398]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.1821924892° = 112°10'55″ = 1.1843648703 rad
∠ B' = β' = 120.3266408408° = 120°19'35″ = 1.04215006498 rad
∠ C' = γ' = 127.49216667° = 127°29'30″ = 0.91664433008 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 = 441.59 ; ; b = 411.63 ; ; c = 378.38 ; ;

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

p = a+b+c = 441.59+411.63+378.38 = 1231.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1231.6 }{ 2 } = 615.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 615.8 * (615.8-441.59)(615.8-411.63)(615.8-378.38) } ; ; T = sqrt{ 5200203757.48 } = 72112.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72112.44 }{ 441.59 } = 326.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72112.44 }{ 411.63 } = 350.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72112.44 }{ 378.38 } = 381.16 ; ;

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{ 441.59**2-411.63**2-378.38**2 }{ 2 * 411.63 * 378.38 } ) = 67° 49'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 411.63**2-441.59**2-378.38**2 }{ 2 * 441.59 * 378.38 } ) = 59° 40'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 378.38**2-441.59**2-411.63**2 }{ 2 * 411.63 * 441.59 } ) = 52° 30'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72112.44 }{ 615.8 } = 117.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 441.59 }{ 2 * sin 67° 49'5" } = 238.44 ; ;




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

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