Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.2   b = 11.7   c = 0.8

Area: T = 3.72992953423
Perimeter: p = 24.7
Semiperimeter: s = 12.35

Angle ∠ A = α = 127.1698899656° = 127°10'8″ = 2.22195160051 rad
Angle ∠ B = β = 49.83658609182° = 49°50'9″ = 0.87697998586 rad
Angle ∠ C = γ = 2.99552394258° = 2°59'43″ = 0.05222767899 rad

Height: ha = 0.61113598922
Height: hb = 0.63774863833
Height: hc = 9.32332383557

Median: ma = 5.61773837327
Median: mb = 6.3655335812
Median: mc = 11.94659198055

Inradius: r = 0.30219672342
Circumradius: R = 7.65550654694

Vertex coordinates: A[0.8; 0] B[0; 0] C[7.869875; 9.32332383557]
Centroid: CG[2.89895833333; 3.10877461186]
Coordinates of the circumscribed circle: U[0.4; 7.64546077297]
Coordinates of the inscribed circle: I[0.65; 0.30219672342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 52.8311100344° = 52°49'52″ = 2.22195160051 rad
∠ B' = β' = 130.1644139082° = 130°9'51″ = 0.87697998586 rad
∠ C' = γ' = 177.0054760574° = 177°17″ = 0.05222767899 rad

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How did we calculate this triangle?

a = 12.2 ; ; b = 11.7 ; ; c = 0.8 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12.2+11.7+0.8 = 24.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.7 }{ 2 } = 12.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.35 * (12.35-12.2)(12.35-11.7)(12.35-0.8) } ; ; T = sqrt{ 13.91 } = 3.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.73 }{ 12.2 } = 0.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.73 }{ 11.7 } = 0.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.73 }{ 0.8 } = 9.32 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 12.2**2-11.7**2-0.8**2 }{ 2 * 11.7 * 0.8 } ) = 127° 10'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11.7**2-12.2**2-0.8**2 }{ 2 * 12.2 * 0.8 } ) = 49° 50'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.8**2-12.2**2-11.7**2 }{ 2 * 11.7 * 12.2 } ) = 2° 59'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.73 }{ 12.35 } = 0.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.2 }{ 2 * sin 127° 10'8" } = 7.66 ; ;

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