Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 478.63   b = 477.94   c = 223.31

Area: T = 51927.09546252
Perimeter: p = 1179.88
Semiperimeter: s = 589.94

Angle ∠ A = α = 76.67220123447° = 76°40'19″ = 1.33881790595 rad
Angle ∠ B = β = 76.32877215° = 76°19'40″ = 1.33221700507 rad
Angle ∠ C = γ = 277.0002661553° = 27°1″ = 0.47112435433 rad

Height: ha = 216.9822197627
Height: hb = 217.2955453928
Height: hc = 465.0677346963

Median: ma = 286.1398656293
Median: mb = 287.0022361663
Median: mc = 465.0769695019

Inradius: r = 88.02109760741
Circumradius: R = 245.9399027642

Vertex coordinates: A[223.31; 0] B[0; 0] C[113.1332840894; 465.0677346963]
Centroid: CG[112.1487613631; 155.0222448988]
Coordinates of the circumscribed circle: U[111.655; 219.1332759514]
Coordinates of the inscribed circle: I[112; 88.02109760741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.3287987655° = 103°19'41″ = 1.33881790595 rad
∠ B' = β' = 103.67222785° = 103°40'20″ = 1.33221700507 rad
∠ C' = γ' = 1532.999733845° = 152°59'59″ = 0.47112435433 rad

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How did we calculate this triangle?

a = 478.63 ; ; b = 477.94 ; ; c = 223.31 ; ;

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

p = a+b+c = 478.63+477.94+223.31 = 1179.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1179.88 }{ 2 } = 589.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 589.94 * (589.94-478.63)(589.94-477.94)(589.94-223.31) } ; ; T = sqrt{ 2696423156.21 } = 51927.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51927.09 }{ 478.63 } = 216.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51927.09 }{ 477.94 } = 217.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51927.09 }{ 223.31 } = 465.07 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 477.94**2+223.31**2-478.63**2 }{ 2 * 477.94 * 223.31 } ) = 76° 40'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 478.63**2+223.31**2-477.94**2 }{ 2 * 478.63 * 223.31 } ) = 76° 19'40" ; ; gamma = 180° - alpha - beta = 180° - 76° 40'19" - 76° 19'40" = 27° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51927.09 }{ 589.94 } = 88.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 478.63 }{ 2 * sin 76° 40'19" } = 245.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 477.94**2+2 * 223.31**2 - 478.63**2 } }{ 2 } = 286.139 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 223.31**2+2 * 478.63**2 - 477.94**2 } }{ 2 } = 287.002 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 477.94**2+2 * 478.63**2 - 223.31**2 } }{ 2 } = 465.07 ; ;
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