100 90 11.17 triangle

Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 11.17

Area: T = 235.9910850139
Perimeter: p = 201.17
Semiperimeter: s = 100.585

Angle ∠ A = α = 151.9998583893° = 151°59'55″ = 2.65328757473 rad
Angle ∠ B = β = 24.9955308303° = 24°59'43″ = 0.43662504274 rad
Angle ∠ C = γ = 3.0066107804° = 3°22″ = 0.05224664788 rad

Height: ha = 4.72198170028
Height: hb = 5.24442411142
Height: hc = 42.25444046803

Median: ma = 40.1554507219
Median: mb = 55.11224709118
Median: mc = 94.96774037499

Inradius: r = 2.34661833289
Circumradius: R = 106.498777305

Vertex coordinates: A[11.17; 0] B[0; 0] C[90.63442390331; 42.25444046803]
Centroid: CG[33.93547463444; 14.08548015601]
Coordinates of the circumscribed circle: U[5.585; 106.3511226789]
Coordinates of the inscribed circle: I[10.585; 2.34661833289]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 28.0011416107° = 28°5″ = 2.65328757473 rad
∠ B' = β' = 155.0054691697° = 155°17″ = 0.43662504274 rad
∠ C' = γ' = 176.9943892196° = 176°59'38″ = 0.05224664788 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 = 100+90+11.17 = 201.17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 201.17 }{ 2 } = 100.59 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 100.59 * (100.59-100)(100.59-90)(100.59-11.17) } ; ; T = sqrt{ 55691.68 } = 235.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 235.99 }{ 100 } = 4.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 235.99 }{ 90 } = 5.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 235.99 }{ 11.17 } = 42.25 ; ;

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{ 90**2+11.17**2-100**2 }{ 2 * 90 * 11.17 } ) = 151° 59'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+11.17**2-90**2 }{ 2 * 100 * 11.17 } ) = 24° 59'43" ; ;
 gamma = 180° - alpha - beta = 180° - 151° 59'55" - 24° 59'43" = 3° 22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 235.99 }{ 100.59 } = 2.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 151° 59'55" } = 106.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 11.17**2 - 100**2 } }{ 2 } = 40.155 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.17**2+2 * 100**2 - 90**2 } }{ 2 } = 55.112 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 11.17**2 } }{ 2 } = 94.967 ; ;
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