Triangle calculator

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 93.5 b = 121.3 c = 207.8220394

Area: T = 2796.392154589
Perimeter: p = 422.6220394
Semiperimeter: s = 211.3110197

Angle ∠ A = α = 12.81883033513° = 12°49'6″ = 0.2243721598 rad
Angle ∠ B = β = 16.72877742945° = 16°43'40″ = 0.2921954738 rad
Angle ∠ C = γ = 150.4543922354° = 150°27'14″ = 2.62659163176 rad

Height: h_a = 59.81658619441
Height: h_b = 46.10770329083
Height: h_c = 26.91216181724

Median: m_a = 163.6032996859
Median: m_b = 149.2989519328
Median: m_c = 30.50664084976

Inradius: r = 13.23435854378
Circumradius: R = 210.7188469758

Vertex coordinates: A[207.8220394; 0] B[0; 0] C[89.54333683046; 26.91216181724]
Centroid: CG[99.12112541015; 8.97105393908]
Coordinates of the circumscribed circle: U[103.9110197; -183.3176514413]
Coordinates of the inscribed circle: I[90.0110197; 13.23435854378]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.1821696649° = 167°10'54″ = 0.2243721598 rad
∠ B' = β' = 163.2722225705° = 163°16'20″ = 0.2921954738 rad
∠ C' = γ' = 29.54660776458° = 29°32'46″ = 2.62659163176 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.

$a = 93.5 ; ; b = 121.3 ; ; c = 207.82 ; ;$

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

$p = a+b+c = 93.5+121.3+207.82 = 422.62 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 422.62 }{ 2 } = 211.31 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 211.31 * (211.31-93.5)(211.31-121.3)(211.31-207.82) } ; ; T = sqrt{ 7819805.68 } = 2796.39 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2796.39 }{ 93.5 } = 59.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2796.39 }{ 121.3 } = 46.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2796.39 }{ 207.82 } = 26.91 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 93.5**2-121.3**2-207.82**2 }{ 2 * 121.3 * 207.82 } ) = 12° 49'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 121.3**2-93.5**2-207.82**2 }{ 2 * 93.5 * 207.82 } ) = 16° 43'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 207.82**2-93.5**2-121.3**2 }{ 2 * 121.3 * 93.5 } ) = 150° 27'14" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 2796.39 }{ 211.31 } = 13.23 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 93.5 }{ 2 * sin 12° 49'6" } = 210.72 ; ;$

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