Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 29.88   b = 413.74   c = 405

Area: T = 5844.606592414
Perimeter: p = 848.62
Semiperimeter: s = 424.31

Angle ∠ A = α = 44.0001676997° = 4°1″ = 0.0769816097 rad
Angle ∠ B = β = 104.9977126703° = 104°59'50″ = 1.83325455661 rad
Angle ∠ C = γ = 71.00327055972° = 71°10″ = 1.23992309905 rad

Height: ha = 391.2055215806
Height: hb = 28.25325543778
Height: hc = 28.86222514772

Median: ma = 409.1210630377
Median: mb = 199.158750124
Median: mc = 212.2044031536

Inradius: r = 13.77443770454
Circumradius: R = 214.1654705927

Vertex coordinates: A[405; 0] B[0; 0] C[-7.7322065679; 28.86222514772]
Centroid: CG[132.4232644774; 9.62107504924]
Coordinates of the circumscribed circle: U[202.5; 69.71656457661]
Coordinates of the inscribed circle: I[10.57; 13.77443770454]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1765.9998323° = 175°59'59″ = 0.0769816097 rad
∠ B' = β' = 75.00328732969° = 75°10″ = 1.83325455661 rad
∠ C' = γ' = 108.9977294403° = 108°59'50″ = 1.23992309905 rad

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How did we calculate this triangle?

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

p = a+b+c = 29.88+413.74+405 = 848.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 848.62 }{ 2 } = 424.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 424.31 * (424.31-29.88)(424.31-413.74)(424.31-405) } ; ; T = sqrt{ 34159418.41 } = 5844.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5844.61 }{ 29.88 } = 391.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5844.61 }{ 413.74 } = 28.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5844.61 }{ 405 } = 28.86 ; ;

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{ 413.74**2+405**2-29.88**2 }{ 2 * 413.74 * 405 } ) = 4° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 29.88**2+405**2-413.74**2 }{ 2 * 29.88 * 405 } ) = 104° 59'50" ; ;
 gamma = 180° - alpha - beta = 180° - 4° 1" - 104° 59'50" = 71° 10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5844.61 }{ 424.31 } = 13.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 29.88 }{ 2 * sin 4° 1" } = 214.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 413.74**2+2 * 405**2 - 29.88**2 } }{ 2 } = 409.121 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 405**2+2 * 29.88**2 - 413.74**2 } }{ 2 } = 199.158 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 413.74**2+2 * 29.88**2 - 405**2 } }{ 2 } = 212.204 ; ;
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