12 19 29 triangle

Obtuse scalene triangle.

Sides: a = 12 b = 19 c = 29

Area: T = 77.0711395472
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 16.24553430883° = 16°14'43″ = 0.2843534725 rad
Angle ∠ B = β = 26.29215552747° = 26°17'30″ = 0.4598874205 rad
Angle ∠ C = γ = 137.4633101637° = 137°27'47″ = 2.39991837236 rad

Height: h_a = 12.84552325787
Height: h_b = 8.11327784707
Height: h_c = 5.31552686532

Median: m_a = 23.7769728648
Median: m_b = 20.05661711201
Median: m_c = 6.5

Inradius: r = 2.56990465157
Circumradius: R = 21.44876459117

Vertex coordinates: A[29; 0] B[0; 0] C[10.75986206897; 5.31552686532]
Centroid: CG[13.25328735632; 1.77217562177]
Coordinates of the circumscribed circle: U[14.5; -15.80435285665]
Coordinates of the inscribed circle: I[11; 2.56990465157]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7554656912° = 163°45'17″ = 0.2843534725 rad
∠ B' = β' = 153.7088444725° = 153°42'30″ = 0.4598874205 rad
∠ C' = γ' = 42.5376898363° = 42°32'13″ = 2.39991837236 rad

Calculate another triangle

How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

$a = 12 ; ; b = 19 ; ; c = 29 ; ;$

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

$p = a+b+c = 12+19+29 = 60 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-12)(30-19)(30-29) } ; ; T = sqrt{ 5940 } = 77.07 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.07 }{ 12 } = 12.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.07 }{ 19 } = 8.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.07 }{ 29 } = 5.32 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 12**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 16° 14'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 26° 17'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-19**2 }{ 2 * 19 * 12 } ) = 137° 27'47" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.07 }{ 30 } = 2.57 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 16° 14'43" } = 21.45 ; ;$

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