Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 18   b = 21   c = 24

Area: T = 182.9988463108
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 20.33331625676
Height: hb = 17.42884250579
Height: hc = 15.25498719257

Median: ma = 20.67660731281
Median: mb = 18.43223085912
Median: mc = 15.44334452115

Inradius: r = 5.80994750193
Circumradius: R = 12.39435467079

Vertex coordinates: A[24; 0] B[0; 0] C[9.56325; 15.25498719257]
Centroid: CG[11.18875; 5.08332906419]
Coordinates of the circumscribed circle: U[12; 3.0988386677]
Coordinates of the inscribed circle: I[10.5; 5.80994750193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad

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How did we calculate this triangle?

a = 18 ; ; b = 21 ; ; c = 24 ; ;

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

p = a+b+c = 18+21+24 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-18)(31.5-21)(31.5-24) } ; ; T = sqrt{ 33488.44 } = 183 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 183 }{ 18 } = 20.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 183 }{ 21 } = 17.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 183 }{ 24 } = 15.25 ; ;

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**2-21**2-24**2 }{ 2 * 21 * 24 } ) = 46° 34'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 57° 54'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-18**2-21**2 }{ 2 * 21 * 18 } ) = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 183 }{ 31.5 } = 5.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 46° 34'3" } = 12.39 ; ;

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