Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.37   b = 8.06   c = 8.94

Area: T = 35.97108276783
Perimeter: p = 29.37
Semiperimeter: s = 14.685

Angle ∠ A = α = 93.23438897447° = 93°14'2″ = 1.62772383505 rad
Angle ∠ B = β = 40.58222378543° = 40°34'56″ = 0.70882936684 rad
Angle ∠ C = γ = 46.1843872401° = 46°11'2″ = 0.80660606347 rad

Height: ha = 5.81658169245
Height: hb = 8.92657636919
Height: hc = 8.04771650287

Median: ma = 5.8477168118
Median: mb = 10.01114609324
Median: mc = 9.43444766681

Inradius: r = 2.44994945644
Circumradius: R = 6.19548648775

Vertex coordinates: A[8.94; 0] B[0; 0] C[9.39546812081; 8.04771650287]
Centroid: CG[6.11215604027; 2.68223883429]
Coordinates of the circumscribed circle: U[4.47; 4.28989918222]
Coordinates of the inscribed circle: I[6.625; 2.44994945644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 86.76661102553° = 86°45'58″ = 1.62772383505 rad
∠ B' = β' = 139.4187762146° = 139°25'4″ = 0.70882936684 rad
∠ C' = γ' = 133.8166127599° = 133°48'58″ = 0.80660606347 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 = 12.37+8.06+8.94 = 29.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.37 }{ 2 } = 14.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.69 * (14.69-12.37)(14.69-8.06)(14.69-8.94) } ; ; T = sqrt{ 1293.9 } = 35.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.97 }{ 12.37 } = 5.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.97 }{ 8.06 } = 8.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.97 }{ 8.94 } = 8.05 ; ;

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{ 8.06**2+8.94**2-12.37**2 }{ 2 * 8.06 * 8.94 } ) = 93° 14'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.37**2+8.94**2-8.06**2 }{ 2 * 12.37 * 8.94 } ) = 40° 34'56" ; ; gamma = 180° - alpha - beta = 180° - 93° 14'2" - 40° 34'56" = 46° 11'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.97 }{ 14.69 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.37 }{ 2 * sin 93° 14'2" } = 6.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 8.94**2 - 12.37**2 } }{ 2 } = 5.847 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.94**2+2 * 12.37**2 - 8.06**2 } }{ 2 } = 10.011 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 12.37**2 - 8.94**2 } }{ 2 } = 9.434 ; ;
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