Triangle calculator

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

You have entered side b, angle α and angle β.

Obtuse scalene triangle.

Sides: a = 4.18439772164   b = 5.7   c = 8.26990237854

Area: T = 11.00333285735
Perimeter: p = 18.15330010017
Semiperimeter: s = 9.07765005009

Angle ∠ A = α = 27.83333333333° = 27°50' = 0.48657833085 rad
Angle ∠ B = β = 39.5° = 39°30' = 0.68994050545 rad
Angle ∠ C = γ = 112.6676666667° = 112°40' = 1.96664042906 rad

Height: ha = 5.26597459328
Height: hb = 3.86108170433
Height: hc = 2.66113367815

Median: ma = 6.78765278932
Median: mb = 5.90107380771
Median: mc = 2.8111342043

Inradius: r = 1.21222875521
Circumradius: R = 4.48105810184

Vertex coordinates: A[8.26990237854; 0] B[0; 0] C[3.22884596765; 2.66113367815]
Centroid: CG[3.83224944873; 0.88771122605]
Coordinates of the circumscribed circle: U[4.13545118927; -1.7276678219]
Coordinates of the inscribed circle: I[3.37765005009; 1.21222875521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1676666667° = 152°10' = 0.48657833085 rad
∠ B' = β' = 140.5° = 140°30' = 0.68994050545 rad
∠ C' = γ' = 67.33333333333° = 67°20' = 1.96664042906 rad

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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 = 4.18 ; ; b = 5.7 ; ; c = 8.27 ; ;

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

p = a+b+c = 4.18+5.7+8.27 = 18.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.15 }{ 2 } = 9.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.08 * (9.08-4.18)(9.08-5.7)(9.08-8.27) } ; ; T = sqrt{ 121.07 } = 11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11 }{ 4.18 } = 5.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11 }{ 5.7 } = 3.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11 }{ 8.27 } = 2.66 ; ;

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{ 4.18**2-5.7**2-8.27**2 }{ 2 * 5.7 * 8.27 } ) = 27° 50' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.7**2-4.18**2-8.27**2 }{ 2 * 4.18 * 8.27 } ) = 39° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.27**2-4.18**2-5.7**2 }{ 2 * 5.7 * 4.18 } ) = 112° 40' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11 }{ 9.08 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.18 }{ 2 * sin 27° 50' } = 4.48 ; ;




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