Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 51.18   b = 24.34   c = 65

Area: T = 569.0322497476
Perimeter: p = 140.52
Semiperimeter: s = 70.26

Angle ∠ A = α = 465.9998695013° = 46° = 0.80328491783 rad
Angle ∠ B = β = 20.00548861213° = 20°18″ = 0.34991511293 rad
Angle ∠ C = γ = 113.9955244377° = 113°59'43″ = 1.9989592346 rad

Height: ha = 22.23765180725
Height: hb = 46.75769841804
Height: hc = 17.509869223

Median: ma = 41.87992275478
Median: mb = 57.22196408587
Median: mc = 23.44549141606

Inradius: r = 8.09989538496
Circumradius: R = 35.57443645395

Vertex coordinates: A[65; 0] B[0; 0] C[48.09219753846; 17.509869223]
Centroid: CG[37.69773251282; 5.83662307433]
Coordinates of the circumscribed circle: U[32.5; -14.46767001209]
Coordinates of the inscribed circle: I[45.92; 8.09989538496]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1344.000130499° = 134° = 0.80328491783 rad
∠ B' = β' = 159.9955113879° = 159°59'42″ = 0.34991511293 rad
∠ C' = γ' = 66.00547556225° = 66°17″ = 1.9989592346 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 = 51.18+24.34+65 = 140.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 140.52 }{ 2 } = 70.26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 70.26 * (70.26-51.18)(70.26-24.34)(70.26-65) } ; ; T = sqrt{ 323797.98 } = 569.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 569.03 }{ 51.18 } = 22.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 569.03 }{ 24.34 } = 46.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 569.03 }{ 65 } = 17.51 ; ;

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{ 24.34**2+65**2-51.18**2 }{ 2 * 24.34 * 65 } ) = 46° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 51.18**2+65**2-24.34**2 }{ 2 * 51.18 * 65 } ) = 20° 18" ; ; gamma = 180° - alpha - beta = 180° - 46° - 20° 18" = 113° 59'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 569.03 }{ 70.26 } = 8.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 51.18 }{ 2 * sin 46° } = 35.57 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24.34**2+2 * 65**2 - 51.18**2 } }{ 2 } = 41.879 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 51.18**2 - 24.34**2 } }{ 2 } = 57.22 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24.34**2+2 * 51.18**2 - 65**2 } }{ 2 } = 23.445 ; ;
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