Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.22   b = 8.06   c = 7.07

Area: T = 27.49113470597
Perimeter: p = 24.35
Semiperimeter: s = 12.175

Angle ∠ A = α = 74.76993555891° = 74°46'10″ = 1.30549714346 rad
Angle ∠ B = β = 57.51096291213° = 57°30'35″ = 1.00437323798 rad
Angle ∠ C = γ = 47.72110152896° = 47°43'16″ = 0.83328888392 rad

Height: ha = 5.96334158481
Height: hb = 6.82216742084
Height: hc = 7.77769015728

Median: ma = 6.01884840284
Median: mb = 7.15993121178
Median: mc = 7.90550474382

Inradius: r = 2.25880161856
Circumradius: R = 4.77878153873

Vertex coordinates: A[7.07; 0] B[0; 0] C[4.95325954738; 7.77769015728]
Centroid: CG[4.00875318246; 2.59223005243]
Coordinates of the circumscribed circle: U[3.535; 3.21442331706]
Coordinates of the inscribed circle: I[4.115; 2.25880161856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.2310644411° = 105°13'50″ = 1.30549714346 rad
∠ B' = β' = 122.4990370879° = 122°29'25″ = 1.00437323798 rad
∠ C' = γ' = 132.279898471° = 132°16'44″ = 0.83328888392 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 = 9.22+8.06+7.07 = 24.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.35 }{ 2 } = 12.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.18 * (12.18-9.22)(12.18-8.06)(12.18-7.07) } ; ; T = sqrt{ 755.77 } = 27.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.49 }{ 9.22 } = 5.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.49 }{ 8.06 } = 6.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.49 }{ 7.07 } = 7.78 ; ;

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{ 8.06**2+7.07**2-9.22**2 }{ 2 * 8.06 * 7.07 } ) = 74° 46'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.22**2+7.07**2-8.06**2 }{ 2 * 9.22 * 7.07 } ) = 57° 30'35" ; ; gamma = 180° - alpha - beta = 180° - 74° 46'10" - 57° 30'35" = 47° 43'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.49 }{ 12.18 } = 2.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.22 }{ 2 * sin 74° 46'10" } = 4.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 7.07**2 - 9.22**2 } }{ 2 } = 6.018 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 9.22**2 - 8.06**2 } }{ 2 } = 7.159 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 9.22**2 - 7.07**2 } }{ 2 } = 7.905 ; ;
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