Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 125   b = 95   c = 93.2

Area: T = 4396.169926044
Perimeter: p = 313.2
Semiperimeter: s = 156.6

Angle ∠ A = α = 83.23440745589° = 83°14'3″ = 1.45327086509 rad
Angle ∠ B = β = 498.9997894356° = 48°59'59″ = 0.85552076584 rad
Angle ∠ C = γ = 47.76661360055° = 47°45'58″ = 0.83436763443 rad

Height: ha = 70.3398708167
Height: hb = 92.55109317986
Height: hc = 94.33883961467

Median: ma = 70.35217590398
Median: mb = 99.49655777912
Median: mc = 100.7644279385

Inradius: r = 28.07326006414
Circumradius: R = 62.93883182513

Vertex coordinates: A[93.2; 0] B[0; 0] C[82.00877253219; 94.33883961467]
Centroid: CG[58.40325751073; 31.44661320489]
Coordinates of the circumscribed circle: U[46.6; 42.30545139944]
Coordinates of the inscribed circle: I[61.6; 28.07326006414]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96.76659254411° = 96°45'57″ = 1.45327086509 rad
∠ B' = β' = 1311.000210564° = 131°1″ = 0.85552076584 rad
∠ C' = γ' = 132.2343863995° = 132°14'2″ = 0.83436763443 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 = 125+95+93.2 = 313.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 313.2 }{ 2 } = 156.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 156.6 * (156.6-125)(156.6-95)(156.6-93.2) } ; ; T = sqrt{ 19326304.17 } = 4396.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4396.17 }{ 125 } = 70.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4396.17 }{ 95 } = 92.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4396.17 }{ 93.2 } = 94.34 ; ;

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{ 95**2+93.2**2-125**2 }{ 2 * 95 * 93.2 } ) = 83° 14'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 125**2+93.2**2-95**2 }{ 2 * 125 * 93.2 } ) = 48° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 83° 14'3" - 48° 59'59" = 47° 45'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4396.17 }{ 156.6 } = 28.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 125 }{ 2 * sin 83° 14'3" } = 62.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 95**2+2 * 93.2**2 - 125**2 } }{ 2 } = 70.352 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 93.2**2+2 * 125**2 - 95**2 } }{ 2 } = 99.496 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 95**2+2 * 125**2 - 93.2**2 } }{ 2 } = 100.764 ; ;
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