Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.16   b = 7.07   c = 6.32

Area: T = 9.98655898679
Perimeter: p = 16.55
Semiperimeter: s = 8.275

Angle ∠ A = α = 26.54987130733° = 26°32'55″ = 0.46333624553 rad
Angle ∠ B = β = 90.08216208079° = 90°4'54″ = 1.57222208786 rad
Angle ∠ C = γ = 63.37696661188° = 63°22'11″ = 1.10660093197 rad

Height: ha = 6.32199935873
Height: hb = 2.82547778976
Height: hc = 3.16599967936

Median: ma = 6.51766901108
Median: mb = 3.53109736618
Median: mc = 4.47220968236

Inradius: r = 1.20767178088
Circumradius: R = 3.53550035869

Vertex coordinates: A[6.32; 0] B[0; 0] C[-0.00545015823; 3.16599967936]
Centroid: CG[2.10551661392; 1.05333322645]
Coordinates of the circumscribed circle: U[3.16; 1.585450319]
Coordinates of the inscribed circle: I[1.205; 1.20767178088]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4511286927° = 153°27'5″ = 0.46333624553 rad
∠ B' = β' = 89.91883791921° = 89°55'6″ = 1.57222208786 rad
∠ C' = γ' = 116.6330333881° = 116°37'49″ = 1.10660093197 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+7.07+6.32 = 16.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.55 }{ 2 } = 8.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.28 * (8.28-3.16)(8.28-7.07)(8.28-6.32) } ; ; T = sqrt{ 99.71 } = 9.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.99 }{ 3.16 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.99 }{ 7.07 } = 2.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.99 }{ 6.32 } = 3.16 ; ;

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{ 7.07**2+6.32**2-3.16**2 }{ 2 * 7.07 * 6.32 } ) = 26° 32'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.16**2+6.32**2-7.07**2 }{ 2 * 3.16 * 6.32 } ) = 90° 4'54" ; ; gamma = 180° - alpha - beta = 180° - 26° 32'55" - 90° 4'54" = 63° 22'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.99 }{ 8.28 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.16 }{ 2 * sin 26° 32'55" } = 3.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 6.32**2 - 3.16**2 } }{ 2 } = 6.517 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 3.16**2 - 7.07**2 } }{ 2 } = 3.531 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 3.16**2 - 6.32**2 } }{ 2 } = 4.472 ; ;
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