Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 12   b = 28   c = 28

Area: T = 164.0987531974
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 24.74772502324° = 24°44'50″ = 0.43219209974 rad
Angle ∠ B = β = 77.62663748838° = 77°37'35″ = 1.35548358281 rad
Angle ∠ C = γ = 77.62663748838° = 77°37'35″ = 1.35548358281 rad

Height: ha = 27.35495886624
Height: hb = 11.72112522839
Height: hc = 11.72112522839

Median: ma = 27.35495886624
Median: mb = 16.37107055437
Median: mc = 16.37107055437

Inradius: r = 4.82663979992
Circumradius: R = 14.33329395129

Vertex coordinates: A[28; 0] B[0; 0] C[2.57114285714; 11.72112522839]
Centroid: CG[10.19904761905; 3.90770840946]
Coordinates of the circumscribed circle: U[14; 3.07113441813]
Coordinates of the inscribed circle: I[6; 4.82663979992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.2532749768° = 155°15'10″ = 0.43219209974 rad
∠ B' = β' = 102.3743625116° = 102°22'25″ = 1.35548358281 rad
∠ C' = γ' = 102.3743625116° = 102°22'25″ = 1.35548358281 rad

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How did we calculate this triangle?

a = 12 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 12+28+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-12)(34-28)(34-28) } ; ; T = sqrt{ 26928 } = 164.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 164.1 }{ 12 } = 27.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 164.1 }{ 28 } = 11.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 164.1 }{ 28 } = 11.72 ; ;

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{ 28**2+28**2-12**2 }{ 2 * 28 * 28 } ) = 24° 44'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12**2+28**2-28**2 }{ 2 * 12 * 28 } ) = 77° 37'35" ; ; gamma = 180° - alpha - beta = 180° - 24° 44'50" - 77° 37'35" = 77° 37'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 164.1 }{ 34 } = 4.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 24° 44'50" } = 14.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 12**2 } }{ 2 } = 27.35 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 12**2 - 28**2 } }{ 2 } = 16.371 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 12**2 - 28**2 } }{ 2 } = 16.371 ; ;
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