Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 125   b = 95   c = 70.82

Area: T = 3340.545473407
Perimeter: p = 290.82
Semiperimeter: s = 145.41

Angle ∠ A = α = 96.76327258569° = 96°45'46″ = 1.68988281594 rad
Angle ∠ B = β = 499.0002260086° = 49°1″ = 0.85552152781 rad
Angle ∠ C = γ = 34.23770481345° = 34°14'13″ = 0.59875492161 rad

Height: ha = 53.44987157451
Height: hb = 70.32772575593
Height: hc = 94.33990210129

Median: ma = 55.80331020643
Median: mb = 89.87997004449
Median: mc = 105.2199446397

Inradius: r = 22.97332806139
Circumradius: R = 62.93879013716

Vertex coordinates: A[70.82; 0] B[0; 0] C[82.00770064953; 94.33990210129]
Centroid: CG[50.94223354984; 31.44663403376]
Coordinates of the circumscribed circle: U[35.41; 52.03218299607]
Coordinates of the inscribed circle: I[50.41; 22.97332806139]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 83.23772741431° = 83°14'14″ = 1.68988281594 rad
∠ B' = β' = 1310.999773991° = 130°59'59″ = 0.85552152781 rad
∠ C' = γ' = 145.7632951866° = 145°45'47″ = 0.59875492161 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+70.82 = 290.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 290.82 }{ 2 } = 145.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 145.41 * (145.41-125)(145.41-95)(145.41-70.82) } ; ; T = sqrt{ 11159239.12 } = 3340.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3340.54 }{ 125 } = 53.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3340.54 }{ 95 } = 70.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3340.54 }{ 70.82 } = 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+70.82**2-125**2 }{ 2 * 95 * 70.82 } ) = 96° 45'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 125**2+70.82**2-95**2 }{ 2 * 125 * 70.82 } ) = 49° 1" ; ; gamma = 180° - alpha - beta = 180° - 96° 45'46" - 49° 1" = 34° 14'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3340.54 }{ 145.41 } = 22.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 125 }{ 2 * sin 96° 45'46" } = 62.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 95**2+2 * 70.82**2 - 125**2 } }{ 2 } = 55.803 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 70.82**2+2 * 125**2 - 95**2 } }{ 2 } = 89.8 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 95**2+2 * 125**2 - 70.82**2 } }{ 2 } = 105.219 ; ;
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