101.36 158.67 220.25 triangle

Obtuse scalene triangle.

Sides: a = 101.36   b = 158.67   c = 220.25

Area: T = 7348.724413182
Perimeter: p = 480.28
Semiperimeter: s = 240.14

Angle ∠ A = α = 24.87701456524° = 24°52'13″ = 0.43440659271 rad
Angle ∠ B = β = 41.17444533421° = 41°10'28″ = 0.71986297785 rad
Angle ∠ C = γ = 113.9555401005° = 113°57'19″ = 1.9898896948 rad

Height: ha = 145.0022449326
Height: hb = 92.62990304635
Height: hc = 66.73107526158

Median: ma = 185.134414947
Median: mb = 151.9879978369
Median: mc = 74.81663994389

Inradius: r = 30.60218328134
Circumradius: R = 120.505509375

Vertex coordinates: A[220.25; 0] B[0; 0] C[76.29545362089; 66.73107526158]
Centroid: CG[98.84881787363; 22.24435842053]
Coordinates of the circumscribed circle: U[110.125; -48.92881309143]
Coordinates of the inscribed circle: I[81.47; 30.60218328134]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1329854348° = 155°7'47″ = 0.43440659271 rad
∠ B' = β' = 138.8265546658° = 138°49'32″ = 0.71986297785 rad
∠ C' = γ' = 66.04545989946° = 66°2'41″ = 1.9898896948 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 = 101.36+158.67+220.25 = 480.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 480.28 }{ 2 } = 240.14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 240.14 * (240.14-101.36)(240.14-158.67)(240.14-220.25) } ; ; T = sqrt{ 54003746.37 } = 7348.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7348.72 }{ 101.36 } = 145 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7348.72 }{ 158.67 } = 92.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7348.72 }{ 220.25 } = 66.73 ; ;

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{ 158.67**2+220.25**2-101.36**2 }{ 2 * 158.67 * 220.25 } ) = 24° 52'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 101.36**2+220.25**2-158.67**2 }{ 2 * 101.36 * 220.25 } ) = 41° 10'28" ; ; gamma = 180° - alpha - beta = 180° - 24° 52'13" - 41° 10'28" = 113° 57'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7348.72 }{ 240.14 } = 30.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 101.36 }{ 2 * sin 24° 52'13" } = 120.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 158.67**2+2 * 220.25**2 - 101.36**2 } }{ 2 } = 185.134 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 220.25**2+2 * 101.36**2 - 158.67**2 } }{ 2 } = 151.98 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 158.67**2+2 * 101.36**2 - 220.25**2 } }{ 2 } = 74.816 ; ;
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