Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.9   b = 6.5   c = 6.68

Area: T = 8.71440539727
Perimeter: p = 26.08
Semiperimeter: s = 13.04

Angle ∠ A = α = 156.3355251319° = 156°20'7″ = 2.72985648724 rad
Angle ∠ B = β = 11.66884422702° = 11°40'6″ = 0.20436527362 rad
Angle ∠ C = γ = 11.99663064109° = 11°59'47″ = 0.20993750449 rad

Height: ha = 1.35110161198
Height: hb = 2.68112473762
Height: hc = 2.60989981954

Median: ma = 1.35441417946
Median: mb = 9.74444189155
Median: mc = 9.65326887446

Inradius: r = 0.66882556728
Circumradius: R = 16.06993863543

Vertex coordinates: A[6.68; 0] B[0; 0] C[12.63334131737; 2.60989981954]
Centroid: CG[6.43878043912; 0.87696660651]
Coordinates of the circumscribed circle: U[3.34; 15.71884470544]
Coordinates of the inscribed circle: I[6.54; 0.66882556728]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 23.66547486812° = 23°39'53″ = 2.72985648724 rad
∠ B' = β' = 168.332155773° = 168°19'54″ = 0.20436527362 rad
∠ C' = γ' = 168.0043693589° = 168°13″ = 0.20993750449 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 = 12.9+6.5+6.68 = 26.08 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.08 }{ 2 } = 13.04 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.04 * (13.04-12.9)(13.04-6.5)(13.04-6.68) } ; ; T = sqrt{ 75.93 } = 8.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.71 }{ 12.9 } = 1.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.71 }{ 6.5 } = 2.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.71 }{ 6.68 } = 2.61 ; ;

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{ 6.5**2+6.68**2-12.9**2 }{ 2 * 6.5 * 6.68 } ) = 156° 20'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.9**2+6.68**2-6.5**2 }{ 2 * 12.9 * 6.68 } ) = 11° 40'6" ; ; gamma = 180° - alpha - beta = 180° - 156° 20'7" - 11° 40'6" = 11° 59'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.71 }{ 13.04 } = 0.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.9 }{ 2 * sin 156° 20'7" } = 16.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 6.68**2 - 12.9**2 } }{ 2 } = 1.354 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.68**2+2 * 12.9**2 - 6.5**2 } }{ 2 } = 9.744 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 12.9**2 - 6.68**2 } }{ 2 } = 9.653 ; ;
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