Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 6   b = 24   c = 24

Area: T = 71.43552853987
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 82.81992442185° = 82°49'9″ = 1.44554684956 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 23.81217617996
Height: hb = 5.95329404499
Height: hc = 5.95329404499

Median: ma = 23.81217617996
Median: mb = 12.72879220614
Median: mc = 12.72879220614

Inradius: r = 2.64657513111
Circumradius: R = 12.09548631363

Vertex coordinates: A[24; 0] B[0; 0] C[0.75; 5.95329404499]
Centroid: CG[8.25; 1.98443134833]
Coordinates of the circumscribed circle: U[12; 1.5121857892]
Coordinates of the inscribed circle: I[3; 2.64657513111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 97.18107557815° = 97°10'51″ = 1.44554684956 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 rad

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How did we calculate this triangle?

a = 6 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 6+24+24 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-6)(27-24)(27-24) } ; ; T = sqrt{ 5103 } = 71.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.44 }{ 6 } = 23.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.44 }{ 24 } = 5.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.44 }{ 24 } = 5.95 ; ;

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{ 24**2+24**2-6**2 }{ 2 * 24 * 24 } ) = 14° 21'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+24**2-24**2 }{ 2 * 6 * 24 } ) = 82° 49'9" ; ; gamma = 180° - alpha - beta = 180° - 14° 21'41" - 82° 49'9" = 82° 49'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.44 }{ 27 } = 2.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 14° 21'41" } = 12.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 6**2 } }{ 2 } = 23.812 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 6**2 - 24**2 } }{ 2 } = 12.728 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 6**2 - 24**2 } }{ 2 } = 12.728 ; ;
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