Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7   b = 10.71   c = 15.09

Area: T = 33.89882775964
Perimeter: p = 32.8
Semiperimeter: s = 16.4

Angle ∠ A = α = 24.80328385821° = 24°48'10″ = 0.43328911971 rad
Angle ∠ B = β = 39.92884507217° = 39°55'42″ = 0.69768829303 rad
Angle ∠ C = γ = 115.2698710696° = 115°16'7″ = 2.01218185262 rad

Height: ha = 9.68552221704
Height: hb = 6.33302105689
Height: hc = 4.49328134654

Median: ma = 12.60877793445
Median: mb = 10.47327276772
Median: mc = 4.99224968703

Inradius: r = 2.06769681461
Circumradius: R = 8.34333243532

Vertex coordinates: A[15.09; 0] B[0; 0] C[5.36879257787; 4.49328134654]
Centroid: CG[6.81993085929; 1.49876044885]
Coordinates of the circumscribed circle: U[7.545; -3.56114654655]
Coordinates of the inscribed circle: I[5.69; 2.06769681461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1977161418° = 155°11'50″ = 0.43328911971 rad
∠ B' = β' = 140.0721549278° = 140°4'18″ = 0.69768829303 rad
∠ C' = γ' = 64.73112893039° = 64°43'53″ = 2.01218185262 rad

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How did we calculate this triangle?

a = 7 ; ; b = 10.71 ; ; c = 15.09 ; ;

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

p = a+b+c = 7+10.71+15.09 = 32.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.8 }{ 2 } = 16.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.4 * (16.4-7)(16.4-10.71)(16.4-15.09) } ; ; T = sqrt{ 1149.09 } = 33.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.9 }{ 7 } = 9.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.9 }{ 10.71 } = 6.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.9 }{ 15.09 } = 4.49 ; ;

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{ 10.71**2+15.09**2-7**2 }{ 2 * 10.71 * 15.09 } ) = 24° 48'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+15.09**2-10.71**2 }{ 2 * 7 * 15.09 } ) = 39° 55'42" ; ; gamma = 180° - alpha - beta = 180° - 24° 48'10" - 39° 55'42" = 115° 16'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.9 }{ 16.4 } = 2.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 24° 48'10" } = 8.34 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.71**2+2 * 15.09**2 - 7**2 } }{ 2 } = 12.608 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.09**2+2 * 7**2 - 10.71**2 } }{ 2 } = 10.473 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.71**2+2 * 7**2 - 15.09**2 } }{ 2 } = 4.992 ; ;
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