Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 27

Area: T = 65.79108618275
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 21.93302872758
Height: hb = 5.4832571819
Height: hc = 4.87333971724

Median: ma = 25.36773017879
Median: mb = 15.44334452115
Median: mc = 11.12442977306

Inradius: r = 2.30884512922
Circumradius: R = 14.774408827

Vertex coordinates: A[27; 0] B[0; 0] C[3.5; 4.87333971724]
Centroid: CG[10.16766666667; 1.62444657241]
Coordinates of the circumscribed circle: U[13.5; -6.00219733597]
Coordinates of the inscribed circle: I[4.5; 2.30884512922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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+24+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-6)(28.5-24)(28.5-27) } ; ; T = sqrt{ 4328.44 } = 65.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.79 }{ 6 } = 21.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.79 }{ 24 } = 5.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.79 }{ 27 } = 4.87 ; ;

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{ 24**2+27**2-6**2 }{ 2 * 24 * 27 } ) = 11° 42'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+27**2-24**2 }{ 2 * 6 * 27 } ) = 54° 18'53" ; ;
 gamma = 180° - alpha - beta = 180° - 11° 42'57" - 54° 18'53" = 113° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.79 }{ 28.5 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 11° 42'57" } = 14.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 27**2 - 6**2 } }{ 2 } = 25.367 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 6**2 - 24**2 } }{ 2 } = 15.443 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 6**2 - 27**2 } }{ 2 } = 11.124 ; ;
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