Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.07   b = 15.81   c = 14.14

Area: T = 49.98548993757
Perimeter: p = 37.02
Semiperimeter: s = 18.51

Angle ∠ A = α = 26.56332399118° = 26°33'48″ = 0.46436159965 rad
Angle ∠ B = β = 90.0099055468° = 90°33″ = 1.57109543745 rad
Angle ∠ C = γ = 63.42877046203° = 63°25'40″ = 1.10770222826 rad

Height: ha = 14.14399998234
Height: hb = 6.3233200427
Height: hc = 7.07699999117

Median: ma = 14.57657203939
Median: mb = 7.90440005693
Median: mc = 9.99992799741

Inradius: r = 2.77004267626
Circumradius: R = 7.90550000987

Vertex coordinates: A[14.14; 0] B[0; 0] C[-0.00111173975; 7.07699999117]
Centroid: CG[4.71329608675; 2.35766666372]
Coordinates of the circumscribed circle: U[7.07; 3.53661174416]
Coordinates of the inscribed circle: I[2.7; 2.77004267626]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4376760088° = 153°26'12″ = 0.46436159965 rad
∠ B' = β' = 89.9910944532° = 89°59'27″ = 1.57109543745 rad
∠ C' = γ' = 116.572229538° = 116°34'20″ = 1.10770222826 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 = 7.07+15.81+14.14 = 37.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.02 }{ 2 } = 18.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.51 * (18.51-7.07)(18.51-15.81)(18.51-14.14) } ; ; T = sqrt{ 2498.49 } = 49.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.98 }{ 7.07 } = 14.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.98 }{ 15.81 } = 6.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.98 }{ 14.14 } = 7.07 ; ;

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{ 15.81**2+14.14**2-7.07**2 }{ 2 * 15.81 * 14.14 } ) = 26° 33'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.07**2+14.14**2-15.81**2 }{ 2 * 7.07 * 14.14 } ) = 90° 33" ; ;
 gamma = 180° - alpha - beta = 180° - 26° 33'48" - 90° 33" = 63° 25'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.98 }{ 18.51 } = 2.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.07 }{ 2 * sin 26° 33'48" } = 7.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.81**2+2 * 14.14**2 - 7.07**2 } }{ 2 } = 14.576 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.14**2+2 * 7.07**2 - 15.81**2 } }{ 2 } = 7.904 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.81**2+2 * 7.07**2 - 14.14**2 } }{ 2 } = 9.999 ; ;
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