Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 125   b = 150   c = 253.68

Area: T = 6700.343310489
Perimeter: p = 528.68
Semiperimeter: s = 264.34

Angle ∠ A = α = 20.62199602081° = 20°37'12″ = 0.36598861973 rad
Angle ∠ B = β = 24.99989256821° = 24°59'56″ = 0.43663135626 rad
Angle ∠ C = γ = 134.381111411° = 134°22'52″ = 2.34553928937 rad

Height: ha = 107.2055489678
Height: hb = 89.33879080652
Height: hc = 52.82551585059

Median: ma = 198.7987689121
Median: mb = 185.3766026497
Median: mc = 54.5355441687

Inradius: r = 25.34774430842
Circumradius: R = 177.4722254985

Vertex coordinates: A[253.68; 0] B[0; 0] C[113.2899463892; 52.82551585059]
Centroid: CG[122.323315463; 17.60883861686]
Coordinates of the circumscribed circle: U[126.84; -124.1299028392]
Coordinates of the inscribed circle: I[114.34; 25.34774430842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.3880039792° = 159°22'48″ = 0.36598861973 rad
∠ B' = β' = 155.0011074318° = 155°4″ = 0.43663135626 rad
∠ C' = γ' = 45.61988858902° = 45°37'8″ = 2.34553928937 rad

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How did we calculate this triangle?

a = 125 ; ; b = 150 ; ; c = 253.68 ; ;

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

p = a+b+c = 125+150+253.68 = 528.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 528.68 }{ 2 } = 264.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 264.34 * (264.34-125)(264.34-150)(264.34-253.68) } ; ; T = sqrt{ 44894597.72 } = 6700.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6700.34 }{ 125 } = 107.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6700.34 }{ 150 } = 89.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6700.34 }{ 253.68 } = 52.83 ; ;

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{ 150**2+253.68**2-125**2 }{ 2 * 150 * 253.68 } ) = 20° 37'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 125**2+253.68**2-150**2 }{ 2 * 125 * 253.68 } ) = 24° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 20° 37'12" - 24° 59'56" = 134° 22'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6700.34 }{ 264.34 } = 25.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 125 }{ 2 * sin 20° 37'12" } = 177.47 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 150**2+2 * 253.68**2 - 125**2 } }{ 2 } = 198.798 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 253.68**2+2 * 125**2 - 150**2 } }{ 2 } = 185.376 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 150**2+2 * 125**2 - 253.68**2 } }{ 2 } = 54.535 ; ;
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