Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.22   b = 6.08   c = 8.94

Area: T = 25.983258389
Perimeter: p = 24.24
Semiperimeter: s = 12.12

Angle ∠ A = α = 72.94661163702° = 72°56'46″ = 1.27331499072 rad
Angle ∠ B = β = 39.08326067201° = 39°4'57″ = 0.68221201675 rad
Angle ∠ C = γ = 67.97112769097° = 67°58'17″ = 1.18663225789 rad

Height: ha = 5.63661353341
Height: hb = 8.54769025954
Height: hc = 5.81326585884

Median: ma = 6.09985981996
Median: mb = 8.55771256856
Median: mc = 6.4043631782

Inradius: r = 2.14437775487
Circumradius: R = 4.82220275755

Vertex coordinates: A[8.94; 0] B[0; 0] C[7.15769127517; 5.81326585884]
Centroid: CG[5.36656375839; 1.93875528628]
Coordinates of the circumscribed circle: U[4.47; 1.80986044174]
Coordinates of the inscribed circle: I[6.04; 2.14437775487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.054388363° = 107°3'14″ = 1.27331499072 rad
∠ B' = β' = 140.917739328° = 140°55'3″ = 0.68221201675 rad
∠ C' = γ' = 112.029872309° = 112°1'43″ = 1.18663225789 rad

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How did we calculate this triangle?

a = 9.22 ; ; b = 6.08 ; ; c = 8.94 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 9.22+6.08+8.94 = 24.24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.24 }{ 2 } = 12.12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.12 * (12.12-9.22)(12.12-6.08)(12.12-8.94) } ; ; T = sqrt{ 675.09 } = 25.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.98 }{ 9.22 } = 5.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.98 }{ 6.08 } = 8.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.98 }{ 8.94 } = 5.81 ; ;

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{ 6.08**2+8.94**2-9.22**2 }{ 2 * 6.08 * 8.94 } ) = 72° 56'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.22**2+8.94**2-6.08**2 }{ 2 * 9.22 * 8.94 } ) = 39° 4'57" ; ; gamma = 180° - alpha - beta = 180° - 72° 56'46" - 39° 4'57" = 67° 58'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.98 }{ 12.12 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.22 }{ 2 * sin 72° 56'46" } = 4.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.08**2+2 * 8.94**2 - 9.22**2 } }{ 2 } = 6.099 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.94**2+2 * 9.22**2 - 6.08**2 } }{ 2 } = 8.557 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.08**2+2 * 9.22**2 - 8.94**2 } }{ 2 } = 6.404 ; ;
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