Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 55.9   b = 111.8   c = 125

Area: T = 3124.810999097
Perimeter: p = 292.7
Semiperimeter: s = 146.35

Angle ∠ A = α = 26.56441801886° = 26°33'51″ = 0.46436324074 rad
Angle ∠ B = β = 63.43114650674° = 63°25'53″ = 1.10770879148 rad
Angle ∠ C = γ = 90.0044354744° = 90°16″ = 1.57108723314 rad

Height: ha = 111.8799999677
Height: hb = 55.98999998385
Height: hc = 49.99769598556

Median: ma = 115.243286312
Median: mb = 79.05875423347
Median: mc = 62.49661998845

Inradius: r = 21.35216227603
Circumradius: R = 62.55000001805

Vertex coordinates: A[125; 0] B[0; 0] C[25.002228; 49.99769598556]
Centroid: CG[50.001076; 16.66656532852]
Coordinates of the circumscribed circle: U[62.5; -0.00547502888]
Coordinates of the inscribed circle: I[34.55; 21.35216227603]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4365819811° = 153°26'9″ = 0.46436324074 rad
∠ B' = β' = 116.5698534933° = 116°34'7″ = 1.10770879148 rad
∠ C' = γ' = 89.9965645256° = 89°59'44″ = 1.57108723314 rad

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How did we calculate this triangle?

a = 55.9 ; ; b = 111.8 ; ; c = 125 ; ;

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

p = a+b+c = 55.9+111.8+125 = 292.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 292.7 }{ 2 } = 146.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 146.35 * (146.35-55.9)(146.35-111.8)(146.35-125) } ; ; T = sqrt{ 9764437.48 } = 3124.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3124.81 }{ 55.9 } = 111.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3124.81 }{ 111.8 } = 55.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3124.81 }{ 125 } = 50 ; ;

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{ 111.8**2+125**2-55.9**2 }{ 2 * 111.8 * 125 } ) = 26° 33'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 55.9**2+125**2-111.8**2 }{ 2 * 55.9 * 125 } ) = 63° 25'53" ; ; gamma = 180° - alpha - beta = 180° - 26° 33'51" - 63° 25'53" = 90° 16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3124.81 }{ 146.35 } = 21.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 55.9 }{ 2 * sin 26° 33'51" } = 62.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 111.8**2+2 * 125**2 - 55.9**2 } }{ 2 } = 115.243 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 55.9**2 - 111.8**2 } }{ 2 } = 79.058 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 111.8**2+2 * 55.9**2 - 125**2 } }{ 2 } = 62.496 ; ;
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