35 50 80 triangle

Obtuse scalene triangle.

Sides: a = 35   b = 50   c = 80

Area: T = 564.2688054651
Perimeter: p = 165
Semiperimeter: s = 82.5

Angle ∠ A = α = 16.38876115035° = 16°23'15″ = 0.28660177773 rad
Angle ∠ B = β = 23.76989007051° = 23°46'8″ = 0.41548455769 rad
Angle ∠ C = γ = 139.8433487791° = 139°50'37″ = 2.44107292994 rad

Height: ha = 32.24438888372
Height: hb = 22.57107221861
Height: hc = 14.10767013663

Median: ma = 64.37219659479
Median: mb = 56.45879489532
Median: mc = 16.2021851746

Inradius: r = 6.84396127837
Circumradius: R = 62.02772576331

Vertex coordinates: A[80; 0] B[0; 0] C[32.031125; 14.10767013663]
Centroid: CG[37.344375; 4.70222337888]
Coordinates of the circumscribed circle: U[40; -47.40765469053]
Coordinates of the inscribed circle: I[32.5; 6.84396127837]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.6122388497° = 163°36'45″ = 0.28660177773 rad
∠ B' = β' = 156.2311099295° = 156°13'52″ = 0.41548455769 rad
∠ C' = γ' = 40.15765122086° = 40°9'23″ = 2.44107292994 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 = 35+50+80 = 165 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 165 }{ 2 } = 82.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 82.5 * (82.5-35)(82.5-50)(82.5-80) } ; ; T = sqrt{ 318398.44 } = 564.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 564.27 }{ 35 } = 32.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 564.27 }{ 50 } = 22.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 564.27 }{ 80 } = 14.11 ; ;

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{ 50**2+80**2-35**2 }{ 2 * 50 * 80 } ) = 16° 23'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+80**2-50**2 }{ 2 * 35 * 80 } ) = 23° 46'8" ; ; gamma = 180° - alpha - beta = 180° - 16° 23'15" - 23° 46'8" = 139° 50'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 564.27 }{ 82.5 } = 6.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 16° 23'15" } = 62.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 80**2 - 35**2 } }{ 2 } = 64.372 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 35**2 - 50**2 } }{ 2 } = 56.458 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 35**2 - 80**2 } }{ 2 } = 16.202 ; ;
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