Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.01   b = 2.5   c = 8.04

Area: T = 5.04334536019
Perimeter: p = 16.55
Semiperimeter: s = 8.275

Angle ∠ A = α = 30.122155518° = 30°7'18″ = 0.52657203137 rad
Angle ∠ B = β = 12.04991378514° = 12°2'57″ = 0.21102971275 rad
Angle ∠ C = γ = 137.8299306969° = 137°49'46″ = 2.40655752123 rad

Height: ha = 1.67883539441
Height: hb = 4.03547628815
Height: hc = 1.25545904482

Median: ma = 5.14396279048
Median: mb = 6.98770129526
Median: mc = 2.24215731083

Inradius: r = 0.60994807978
Circumradius: R = 5.98880098805

Vertex coordinates: A[8.04; 0] B[0; 0] C[5.87875932836; 1.25545904482]
Centroid: CG[4.63991977612; 0.41881968161]
Coordinates of the circumscribed circle: U[4.02; -4.4388002065]
Coordinates of the inscribed circle: I[5.775; 0.60994807978]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.878844482° = 149°52'42″ = 0.52657203137 rad
∠ B' = β' = 167.9510862149° = 167°57'3″ = 0.21102971275 rad
∠ C' = γ' = 42.17106930314° = 42°10'14″ = 2.40655752123 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 = 6.01+2.5+8.04 = 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 * (8.28-6.01)(8.28-2.5)(8.28-8.04) } ; ; T = sqrt{ 25.44 } = 5.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.04 }{ 6.01 } = 1.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.04 }{ 2.5 } = 4.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.04 }{ 8.04 } = 1.25 ; ;

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{ 2.5**2+8.04**2-6.01**2 }{ 2 * 2.5 * 8.04 } ) = 30° 7'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.01**2+8.04**2-2.5**2 }{ 2 * 6.01 * 8.04 } ) = 12° 2'57" ; ;
 gamma = 180° - alpha - beta = 180° - 30° 7'18" - 12° 2'57" = 137° 49'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.04 }{ 8.28 } = 0.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.01 }{ 2 * sin 30° 7'18" } = 5.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 8.04**2 - 6.01**2 } }{ 2 } = 5.14 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.04**2+2 * 6.01**2 - 2.5**2 } }{ 2 } = 6.987 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 6.01**2 - 8.04**2 } }{ 2 } = 2.242 ; ;
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