Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 18.79   b = 7.62   c = 14.04

Area: T = 47.56876276898
Perimeter: p = 40.45
Semiperimeter: s = 20.225

Angle ∠ A = α = 117.2221992034° = 117°13'19″ = 2.04659097167 rad
Angle ∠ B = β = 21.13881645657° = 21°8'17″ = 0.36989305695 rad
Angle ∠ C = γ = 41.64398434002° = 41°38'23″ = 0.72767523673 rad

Height: ha = 5.06330790516
Height: hb = 12.48549416509
Height: hc = 6.77660153404

Median: ma = 6.27111223078
Median: mb = 16.14223898479
Median: mc = 12.50113539267

Inradius: r = 2.35219222591
Circumradius: R = 10.56551915474

Vertex coordinates: A[14.04; 0] B[0; 0] C[17.52656873219; 6.77660153404]
Centroid: CG[10.5221895774; 2.25986717801]
Coordinates of the circumscribed circle: U[7.02; 7.89657502768]
Coordinates of the inscribed circle: I[12.605; 2.35219222591]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 62.77880079658° = 62°46'41″ = 2.04659097167 rad
∠ B' = β' = 158.8621835434° = 158°51'43″ = 0.36989305695 rad
∠ C' = γ' = 138.36601566° = 138°21'37″ = 0.72767523673 rad

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How did we calculate this triangle?

a = 18.79 ; ; b = 7.62 ; ; c = 14.04 ; ;

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

p = a+b+c = 18.79+7.62+14.04 = 40.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40.45 }{ 2 } = 20.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.23 * (20.23-18.79)(20.23-7.62)(20.23-14.04) } ; ; T = sqrt{ 2262.68 } = 47.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.57 }{ 18.79 } = 5.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.57 }{ 7.62 } = 12.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.57 }{ 14.04 } = 6.78 ; ;

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{ 18.79**2-7.62**2-14.04**2 }{ 2 * 7.62 * 14.04 } ) = 117° 13'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.62**2-18.79**2-14.04**2 }{ 2 * 18.79 * 14.04 } ) = 21° 8'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.04**2-18.79**2-7.62**2 }{ 2 * 7.62 * 18.79 } ) = 41° 38'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.57 }{ 20.23 } = 2.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.79 }{ 2 * sin 117° 13'19" } = 10.57 ; ;

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