Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 14   b = 29   c = 29

Area: T = 196.9977461913
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 27.93659253493° = 27°56'9″ = 0.48875738769 rad
Angle ∠ B = β = 76.03220373253° = 76°1'55″ = 1.32770093883 rad
Angle ∠ C = γ = 76.03220373253° = 76°1'55″ = 1.32770093883 rad

Height: ha = 28.14224945589
Height: hb = 13.5866031856
Height: hc = 13.5866031856

Median: ma = 28.14224945589
Median: mb = 17.55770498661
Median: mc = 17.55770498661

Inradius: r = 5.47221517198
Circumradius: R = 14.94218168713

Vertex coordinates: A[29; 0] B[0; 0] C[3.37993103448; 13.5866031856]
Centroid: CG[10.79331034483; 4.52986772853]
Coordinates of the circumscribed circle: U[14.5; 3.60766454517]
Coordinates of the inscribed circle: I[7; 5.47221517198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.0644074651° = 152°3'51″ = 0.48875738769 rad
∠ B' = β' = 103.9687962675° = 103°58'5″ = 1.32770093883 rad
∠ C' = γ' = 103.9687962675° = 103°58'5″ = 1.32770093883 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 = 14+29+29 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-14)(36-29)(36-29) } ; ; T = sqrt{ 38808 } = 197 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197 }{ 14 } = 28.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197 }{ 29 } = 13.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197 }{ 29 } = 13.59 ; ;

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{ 29**2+29**2-14**2 }{ 2 * 29 * 29 } ) = 27° 56'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+29**2-29**2 }{ 2 * 14 * 29 } ) = 76° 1'55" ; ; gamma = 180° - alpha - beta = 180° - 27° 56'9" - 76° 1'55" = 76° 1'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197 }{ 36 } = 5.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 27° 56'9" } = 14.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 29**2 - 14**2 } }{ 2 } = 28.142 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 14**2 - 29**2 } }{ 2 } = 17.557 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 14**2 - 29**2 } }{ 2 } = 17.557 ; ;
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