Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.16   b = 1.41   c = 2.83

Area: T = 1.99551479644
Perimeter: p = 7.4
Semiperimeter: s = 3.7

Angle ∠ A = α = 89.91881550123° = 89°55'5″ = 1.56993678623 rad
Angle ∠ B = β = 26.55002729464° = 26°30'1″ = 0.46325170156 rad
Angle ∠ C = γ = 63.58215720413° = 63°34'54″ = 1.11097077757 rad

Height: ha = 1.26327518762
Height: hb = 2.83299971127
Height: hc = 1.41099985614

Median: ma = 1.5821802769
Median: mb = 2.91655145343
Median: mc = 1.99661525493

Inradius: r = 0.53992291796
Circumradius: R = 1.5880001612

Vertex coordinates: A[2.83; 0] B[0; 0] C[2.82879858657; 1.41099985614]
Centroid: CG[1.88659952886; 0.47699995205]
Coordinates of the circumscribed circle: U[1.415; 0.70329794406]
Coordinates of the inscribed circle: I[2.29; 0.53992291796]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.08218449877° = 90°4'55″ = 1.56993678623 rad
∠ B' = β' = 153.5499727054° = 153°29'59″ = 0.46325170156 rad
∠ C' = γ' = 116.4188427959° = 116°25'6″ = 1.11097077757 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 = 3.16+1.41+2.83 = 7.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.4 }{ 2 } = 3.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.7 * (3.7-3.16)(3.7-1.41)(3.7-2.83) } ; ; T = sqrt{ 3.98 } = 2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2 }{ 3.16 } = 1.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2 }{ 1.41 } = 2.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2 }{ 2.83 } = 1.41 ; ;

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{ 1.41**2+2.83**2-3.16**2 }{ 2 * 1.41 * 2.83 } ) = 89° 55'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.16**2+2.83**2-1.41**2 }{ 2 * 3.16 * 2.83 } ) = 26° 30'1" ; ; gamma = 180° - alpha - beta = 180° - 89° 55'5" - 26° 30'1" = 63° 34'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2 }{ 3.7 } = 0.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.16 }{ 2 * sin 89° 55'5" } = 1.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 2.83**2 - 3.16**2 } }{ 2 } = 1.582 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.83**2+2 * 3.16**2 - 1.41**2 } }{ 2 } = 2.916 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 3.16**2 - 2.83**2 } }{ 2 } = 1.996 ; ;
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