Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 22.42   b = 16.8   c = 6.24

Area: T = 26.24993309993
Perimeter: p = 45.46
Semiperimeter: s = 22.73

Angle ∠ A = α = 149.9487818293° = 149°56'52″ = 2.61770831354 rad
Angle ∠ B = β = 22.04401570205° = 22°2'25″ = 0.38546733077 rad
Angle ∠ C = γ = 8.01220246869° = 8°43″ = 0.14398362105 rad

Height: ha = 2.34215995539
Height: hb = 3.12549203571
Height: hc = 8.41332471152

Median: ma = 5.91097123449
Median: mb = 14.15105123582
Median: mc = 19.56330723558

Inradius: r = 1.15548319841
Circumradius: R = 22.38546984906

Vertex coordinates: A[6.24; 0] B[0; 0] C[20.78215705128; 8.41332471152]
Centroid: CG[9.00771901709; 2.80444157051]
Coordinates of the circumscribed circle: U[3.12; 22.16661978363]
Coordinates of the inscribed circle: I[5.93; 1.15548319841]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.05221817074° = 30°3'8″ = 2.61770831354 rad
∠ B' = β' = 157.9659842979° = 157°57'35″ = 0.38546733077 rad
∠ C' = γ' = 171.9887975313° = 171°59'17″ = 0.14398362105 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 = 22.42+16.8+6.24 = 45.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45.46 }{ 2 } = 22.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.73 * (22.73-22.42)(22.73-16.8)(22.73-6.24) } ; ; T = sqrt{ 689.03 } = 26.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.25 }{ 22.42 } = 2.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.25 }{ 16.8 } = 3.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.25 }{ 6.24 } = 8.41 ; ;

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{ 16.8**2+6.24**2-22.42**2 }{ 2 * 16.8 * 6.24 } ) = 149° 56'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22.42**2+6.24**2-16.8**2 }{ 2 * 22.42 * 6.24 } ) = 22° 2'25" ; ;
 gamma = 180° - alpha - beta = 180° - 149° 56'52" - 22° 2'25" = 8° 43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.25 }{ 22.73 } = 1.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22.42 }{ 2 * sin 149° 56'52" } = 22.38 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.8**2+2 * 6.24**2 - 22.42**2 } }{ 2 } = 5.91 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.24**2+2 * 22.42**2 - 16.8**2 } }{ 2 } = 14.151 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.8**2+2 * 22.42**2 - 6.24**2 } }{ 2 } = 19.563 ; ;
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