Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 13.07   b = 5.41   c = 14.14

Area: T = 35.35443292003
Perimeter: p = 32.62
Semiperimeter: s = 16.31

Angle ∠ A = α = 67.56771807458° = 67°34'2″ = 1.17992697703 rad
Angle ∠ B = β = 22.49549698404° = 22°29'42″ = 0.39326112889 rad
Angle ∠ C = γ = 89.93878494139° = 89°56'16″ = 1.57697115944 rad

Height: ha = 5.41099968172
Height: hb = 13.07699923106
Height: hc = 5.00106123338

Median: ma = 8.47992467236
Median: mb = 13.34441082505
Median: mc = 7.07554222489

Inradius: r = 2.16876474065
Circumradius: R = 7.07700041594

Vertex coordinates: A[14.14; 0] B[0; 0] C[12.07655445545; 5.00106123338]
Centroid: CG[8.73985148515; 1.66768707779]
Coordinates of the circumscribed circle: U[7.07; 0.00876690608]
Coordinates of the inscribed circle: I[10.9; 2.16876474065]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.4332819254° = 112°25'58″ = 1.17992697703 rad
∠ B' = β' = 157.505503016° = 157°30'18″ = 0.39326112889 rad
∠ C' = γ' = 90.06221505861° = 90°3'44″ = 1.57697115944 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 = 13.07+5.41+14.14 = 32.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.62 }{ 2 } = 16.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.31 * (16.31-13.07)(16.31-5.41)(16.31-14.14) } ; ; T = sqrt{ 1249.93 } = 35.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.35 }{ 13.07 } = 5.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.35 }{ 5.41 } = 13.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.35 }{ 14.14 } = 5 ; ;

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{ 5.41**2+14.14**2-13.07**2 }{ 2 * 5.41 * 14.14 } ) = 67° 34'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.07**2+14.14**2-5.41**2 }{ 2 * 13.07 * 14.14 } ) = 22° 29'42" ; ; gamma = 180° - alpha - beta = 180° - 67° 34'2" - 22° 29'42" = 89° 56'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.35 }{ 16.31 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.07 }{ 2 * sin 67° 34'2" } = 7.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.41**2+2 * 14.14**2 - 13.07**2 } }{ 2 } = 8.479 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.14**2+2 * 13.07**2 - 5.41**2 } }{ 2 } = 13.344 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.41**2+2 * 13.07**2 - 14.14**2 } }{ 2 } = 7.075 ; ;
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