Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 6   b = 26   c = 26

Area: T = 77.47990294209
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 13.25216191296° = 13°15'6″ = 0.2311284385 rad
Angle ∠ B = β = 83.37441904352° = 83°22'27″ = 1.45551541343 rad
Angle ∠ C = γ = 83.37441904352° = 83°22'27″ = 1.45551541343 rad

Height: ha = 25.82663431403
Height: hb = 5.96599253401
Height: hc = 5.96599253401

Median: ma = 25.82663431403
Median: mb = 13.67547943312
Median: mc = 13.67547943312

Inradius: r = 2.67216906697
Circumradius: R = 13.0877412266

Vertex coordinates: A[26; 0] B[0; 0] C[0.69223076923; 5.96599253401]
Centroid: CG[8.89774358974; 1.987664178]
Coordinates of the circumscribed circle: U[13; 1.51100860307]
Coordinates of the inscribed circle: I[3; 2.67216906697]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.748838087° = 166°44'54″ = 0.2311284385 rad
∠ B' = β' = 96.62658095648° = 96°37'33″ = 1.45551541343 rad
∠ C' = γ' = 96.62658095648° = 96°37'33″ = 1.45551541343 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+26+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-6)(29-26)(29-26) } ; ; T = sqrt{ 6003 } = 77.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.48 }{ 6 } = 25.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.48 }{ 26 } = 5.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.48 }{ 26 } = 5.96 ; ;

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{ 26**2+26**2-6**2 }{ 2 * 26 * 26 } ) = 13° 15'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+26**2-26**2 }{ 2 * 6 * 26 } ) = 83° 22'27" ; ; gamma = 180° - alpha - beta = 180° - 13° 15'6" - 83° 22'27" = 83° 22'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.48 }{ 29 } = 2.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 13° 15'6" } = 13.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 26**2 - 6**2 } }{ 2 } = 25.826 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 6**2 - 26**2 } }{ 2 } = 13.675 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 6**2 - 26**2 } }{ 2 } = 13.675 ; ;
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