Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.8   b = 4.5   c = 10.67

Area: T = 9.6910764259
Perimeter: p = 21.97
Semiperimeter: s = 10.985

Angle ∠ A = α = 23.80769138894° = 23°48'25″ = 0.41655090321 rad
Angle ∠ B = β = 15.49332647179° = 15°29'36″ = 0.27704084812 rad
Angle ∠ C = γ = 140.7699821393° = 140°41'59″ = 2.45656751403 rad

Height: ha = 2.85502247821
Height: hb = 4.30770063374
Height: hc = 1.81664506577

Median: ma = 7.44991241096
Median: mb = 8.65992118579
Median: mc = 2.18769556466

Inradius: r = 0.88221815438
Circumradius: R = 8.42330198793

Vertex coordinates: A[10.67; 0] B[0; 0] C[6.5532900656; 1.81664506577]
Centroid: CG[5.74109668853; 0.60554835526]
Coordinates of the circumscribed circle: U[5.335; -6.51880548393]
Coordinates of the inscribed circle: I[6.485; 0.88221815438]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1933086111° = 156°11'35″ = 0.41655090321 rad
∠ B' = β' = 164.5076735282° = 164°30'24″ = 0.27704084812 rad
∠ C' = γ' = 39.33001786073° = 39°18'1″ = 2.45656751403 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 = 6.8+4.5+10.67 = 21.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.97 }{ 2 } = 10.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.99 * (10.99-6.8)(10.99-4.5)(10.99-10.67) } ; ; T = sqrt{ 93.91 } = 9.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.69 }{ 6.8 } = 2.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.69 }{ 4.5 } = 4.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.69 }{ 10.67 } = 1.82 ; ;

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{ 4.5**2+10.67**2-6.8**2 }{ 2 * 4.5 * 10.67 } ) = 23° 48'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.8**2+10.67**2-4.5**2 }{ 2 * 6.8 * 10.67 } ) = 15° 29'36" ; ; gamma = 180° - alpha - beta = 180° - 23° 48'25" - 15° 29'36" = 140° 41'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.69 }{ 10.99 } = 0.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.8 }{ 2 * sin 23° 48'25" } = 8.42 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 10.67**2 - 6.8**2 } }{ 2 } = 7.449 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.67**2+2 * 6.8**2 - 4.5**2 } }{ 2 } = 8.659 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 6.8**2 - 10.67**2 } }{ 2 } = 2.187 ; ;
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