Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 20   b = 27   c = 30

Area: T = 263.8610640301
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 40.65553767418° = 40°39'19″ = 0.71095701828 rad
Angle ∠ B = β = 61.58663778464° = 61°35'11″ = 1.07548850678 rad
Angle ∠ C = γ = 77.75882454118° = 77°45'30″ = 1.3577137403 rad

Height: ha = 26.38660640301
Height: hb = 19.54552326149
Height: hc = 17.59107093534

Median: ma = 26.73301328092
Median: mb = 21.62875287539
Median: mc = 18.42655257727

Inradius: r = 6.85435231247
Circumradius: R = 15.3499011491

Vertex coordinates: A[30; 0] B[0; 0] C[9.51766666667; 17.59107093534]
Centroid: CG[13.17222222222; 5.86435697845]
Coordinates of the circumscribed circle: U[15; 3.2554558918]
Coordinates of the inscribed circle: I[11.5; 6.85435231247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.3454623258° = 139°20'41″ = 0.71095701828 rad
∠ B' = β' = 118.4143622154° = 118°24'49″ = 1.07548850678 rad
∠ C' = γ' = 102.2421754588° = 102°14'30″ = 1.3577137403 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 = 20+27+30 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-20)(38.5-27)(38.5-30) } ; ; T = sqrt{ 69622.44 } = 263.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 263.86 }{ 20 } = 26.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 263.86 }{ 27 } = 19.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 263.86 }{ 30 } = 17.59 ; ;

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{ 27**2+30**2-20**2 }{ 2 * 27 * 30 } ) = 40° 39'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+30**2-27**2 }{ 2 * 20 * 30 } ) = 61° 35'11" ; ; gamma = 180° - alpha - beta = 180° - 40° 39'19" - 61° 35'11" = 77° 45'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 263.86 }{ 38.5 } = 6.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 40° 39'19" } = 15.35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 30**2 - 20**2 } }{ 2 } = 26.73 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 20**2 - 27**2 } }{ 2 } = 21.628 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 20**2 - 30**2 } }{ 2 } = 18.426 ; ;
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