123 182 105 triangle

Obtuse scalene triangle.

Sides: a = 123   b = 182   c = 105

Area: T = 6217.958786412
Perimeter: p = 410
Semiperimeter: s = 205

Angle ∠ A = α = 40.59985011963° = 40°35'55″ = 0.70985775172 rad
Angle ∠ B = β = 105.6554821704° = 105°39'17″ = 1.84440245093 rad
Angle ∠ C = γ = 33.74766771001° = 33°44'48″ = 0.5898990627 rad

Height: ha = 101.1055005921
Height: hb = 68.3299207298
Height: hc = 118.437729265

Median: ma = 135.2498844727
Median: mb = 69.25331587727
Median: mc = 146.1865669612

Inradius: r = 30.33215017762
Circumradius: R = 94.50657063495

Vertex coordinates: A[105; 0] B[0; 0] C[-33.19904761905; 118.437729265]
Centroid: CG[23.93765079365; 39.479909755]
Coordinates of the circumscribed circle: U[52.5; 78.58216679169]
Coordinates of the inscribed circle: I[23; 30.33215017762]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.4011498804° = 139°24'5″ = 0.70985775172 rad
∠ B' = β' = 74.34551782964° = 74°20'43″ = 1.84440245093 rad
∠ C' = γ' = 146.25333229° = 146°15'12″ = 0.5898990627 rad

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How did we calculate this triangle?

a = 123 ; ; b = 182 ; ; c = 105 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 123+182+105 = 410 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 410 }{ 2 } = 205 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 205 * (205-123)(205-182)(205-105) } ; ; T = sqrt{ 38663000 } = 6217.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6217.96 }{ 123 } = 101.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6217.96 }{ 182 } = 68.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6217.96 }{ 105 } = 118.44 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 123**2-182**2-105**2 }{ 2 * 182 * 105 } ) = 40° 35'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 182**2-123**2-105**2 }{ 2 * 123 * 105 } ) = 105° 39'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 105**2-123**2-182**2 }{ 2 * 182 * 123 } ) = 33° 44'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6217.96 }{ 205 } = 30.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 123 }{ 2 * sin 40° 35'55" } = 94.51 ; ;




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