Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 18   b = 20   c = 22

Area: T = 169.7065627485
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 50.47988036414° = 50°28'44″ = 0.8811021326 rad
Angle ∠ B = β = 58.99224169931° = 58°59'33″ = 1.03296119102 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 18.85661808316
Height: hb = 16.97105627485
Height: hc = 15.42877843168

Median: ma = 19
Median: mb = 17.43655957742
Median: mc = 15.52441746963

Inradius: r = 5.65768542495
Circumradius: R = 11.66772618896

Vertex coordinates: A[22; 0] B[0; 0] C[9.27327272727; 15.42877843168]
Centroid: CG[10.42442424242; 5.14325947723]
Coordinates of the circumscribed circle: U[11; 3.88990872965]
Coordinates of the inscribed circle: I[10; 5.65768542495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.5211196359° = 129°31'16″ = 0.8811021326 rad
∠ B' = β' = 121.0087583007° = 121°27″ = 1.03296119102 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 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 = 18+20+22 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-18)(30-20)(30-22) } ; ; T = sqrt{ 28800 } = 169.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.71 }{ 18 } = 18.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.71 }{ 20 } = 16.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.71 }{ 22 } = 15.43 ; ;

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{ 20**2+22**2-18**2 }{ 2 * 20 * 22 } ) = 50° 28'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+22**2-20**2 }{ 2 * 18 * 22 } ) = 58° 59'33" ; ; gamma = 180° - alpha - beta = 180° - 50° 28'44" - 58° 59'33" = 70° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.71 }{ 30 } = 5.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 50° 28'44" } = 11.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 22**2 - 18**2 } }{ 2 } = 19 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 18**2 - 20**2 } }{ 2 } = 17.436 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 18**2 - 22**2 } }{ 2 } = 15.524 ; ;
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