Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13   b = 14   c = 20

Area: T = 90.57883500623
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 40.31549091747° = 40°18'54″ = 0.70436279027 rad
Angle ∠ B = β = 44.16773564515° = 44°10'2″ = 0.7710865792 rad
Angle ∠ C = γ = 95.51877343738° = 95°31'4″ = 1.66770989589 rad

Height: ha = 13.93551307788
Height: hb = 12.94397642946
Height: hc = 9.05878350062

Median: ma = 15.99221855917
Median: mb = 15.34660092532
Median: mc = 9.08329510623

Inradius: r = 3.8544397875
Circumradius: R = 10.04765508521

Vertex coordinates: A[20; 0] B[0; 0] C[9.325; 9.05878350062]
Centroid: CG[9.775; 3.01992783354]
Coordinates of the circumscribed circle: U[10; -0.9666014505]
Coordinates of the inscribed circle: I[9.5; 3.8544397875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.6855090825° = 139°41'6″ = 0.70436279027 rad
∠ B' = β' = 135.8332643548° = 135°49'58″ = 0.7710865792 rad
∠ C' = γ' = 84.48222656262° = 84°28'56″ = 1.66770989589 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 = 13+14+20 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-13)(23.5-14)(23.5-20) } ; ; T = sqrt{ 8204.44 } = 90.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90.58 }{ 13 } = 13.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90.58 }{ 14 } = 12.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90.58 }{ 20 } = 9.06 ; ;

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{ 14**2+20**2-13**2 }{ 2 * 14 * 20 } ) = 40° 18'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13**2+20**2-14**2 }{ 2 * 13 * 20 } ) = 44° 10'2" ; ;
 gamma = 180° - alpha - beta = 180° - 40° 18'54" - 44° 10'2" = 95° 31'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90.58 }{ 23.5 } = 3.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13 }{ 2 * sin 40° 18'54" } = 10.05 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 20**2 - 13**2 } }{ 2 } = 15.992 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 13**2 - 14**2 } }{ 2 } = 15.346 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 13**2 - 20**2 } }{ 2 } = 9.083 ; ;
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