Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 60   b = 45   c = 22.78

Area: T = 439.3219987002
Perimeter: p = 127.78
Semiperimeter: s = 63.89

Angle ∠ A = α = 121.0054582131° = 121°16″ = 2.11219283682 rad
Angle ∠ B = β = 40.0044261302° = 40°15″ = 0.69882060745 rad
Angle ∠ C = γ = 18.99111565665° = 18°59'28″ = 0.33114582108 rad

Height: ha = 14.64439995667
Height: hb = 19.52553327557
Height: hc = 38.57106748904

Median: ma = 19.28663734279
Median: mb = 39.41108386107
Median: mc = 51.79554428497

Inradius: r = 6.87661932541
Circumradius: R = 35.00106839091

Vertex coordinates: A[22.78; 0] B[0; 0] C[45.96597980685; 38.57106748904]
Centroid: CG[22.91332660228; 12.85768916301]
Coordinates of the circumscribed circle: U[11.39; 33.09655552016]
Coordinates of the inscribed circle: I[18.89; 6.87661932541]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.99554178685° = 58°59'44″ = 2.11219283682 rad
∠ B' = β' = 139.9965738698° = 139°59'45″ = 0.69882060745 rad
∠ C' = γ' = 161.0098843433° = 161°32″ = 0.33114582108 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 = 60+45+22.78 = 127.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 127.78 }{ 2 } = 63.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.89 * (63.89-60)(63.89-45)(63.89-22.78) } ; ; T = sqrt{ 193002.05 } = 439.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 439.32 }{ 60 } = 14.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 439.32 }{ 45 } = 19.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 439.32 }{ 22.78 } = 38.57 ; ;

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{ 45**2+22.78**2-60**2 }{ 2 * 45 * 22.78 } ) = 121° 16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60**2+22.78**2-45**2 }{ 2 * 60 * 22.78 } ) = 40° 15" ; ; gamma = 180° - alpha - beta = 180° - 121° 16" - 40° 15" = 18° 59'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 439.32 }{ 63.89 } = 6.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 121° 16" } = 35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 22.78**2 - 60**2 } }{ 2 } = 19.286 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22.78**2+2 * 60**2 - 45**2 } }{ 2 } = 39.411 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 60**2 - 22.78**2 } }{ 2 } = 51.795 ; ;
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