Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 310   b = 466   c = 400

Area: T = 61230.79553892
Perimeter: p = 1176
Semiperimeter: s = 588

Angle ∠ A = α = 41.07701666127° = 41°4'13″ = 0.71768096317 rad
Angle ∠ B = β = 80.9655320375° = 80°57'55″ = 1.41331114205 rad
Angle ∠ C = γ = 57.96545130122° = 57°57'52″ = 1.01216716014 rad

Height: ha = 395.0377389608
Height: hb = 262.7933113259
Height: hc = 306.1543976946

Median: ma = 405.6511328113
Median: mb = 271.5989764167
Median: mc = 341.5088418637

Inradius: r = 104.1344005764
Circumradius: R = 235.9277034888

Vertex coordinates: A[400; 0] B[0; 0] C[48.68; 306.1543976946]
Centroid: CG[149.56; 102.0511325649]
Coordinates of the circumscribed circle: U[200; 125.1466177692]
Coordinates of the inscribed circle: I[122; 104.1344005764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.9329833387° = 138°55'47″ = 0.71768096317 rad
∠ B' = β' = 99.0354679625° = 99°2'5″ = 1.41331114205 rad
∠ C' = γ' = 122.0355486988° = 122°2'8″ = 1.01216716014 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 = 310 ; ; b = 466 ; ; c = 400 ; ;

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

p = a+b+c = 310+466+400 = 1176 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1176 }{ 2 } = 588 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 588 * (588-310)(588-466)(588-400) } ; ; T = sqrt{ 3749210304 } = 61230.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61230.8 }{ 310 } = 395.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61230.8 }{ 466 } = 262.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61230.8 }{ 400 } = 306.15 ; ;

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{ 310**2-466**2-400**2 }{ 2 * 466 * 400 } ) = 41° 4'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 466**2-310**2-400**2 }{ 2 * 310 * 400 } ) = 80° 57'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 400**2-310**2-466**2 }{ 2 * 466 * 310 } ) = 57° 57'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61230.8 }{ 588 } = 104.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 310 }{ 2 * sin 41° 4'13" } = 235.93 ; ;




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