Triangle calculator SSS - result

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Acute isosceles triangle.

Sides: a = 5.2   b = 5.2   c = 1.56

Area: T = 4.01101104025
Perimeter: p = 11.96
Semiperimeter: s = 5.98

Angle ∠ A = α = 81.37330734413° = 81°22'23″ = 1.4220228054 rad
Angle ∠ B = β = 81.37330734413° = 81°22'23″ = 1.4220228054 rad
Angle ∠ C = γ = 17.25438531174° = 17°15'14″ = 0.30111365456 rad

Height: ha = 1.54223501548
Height: hb = 1.54223501548
Height: hc = 5.14111671827

Median: ma = 2.82443229277
Median: mb = 2.82443229277
Median: mc = 5.14111671827

Inradius: r = 0.67105870238
Circumradius: R = 2.63297530346

Vertex coordinates: A[1.56; 0] B[0; 0] C[0.78; 5.14111671827]
Centroid: CG[0.78; 1.71437223942]
Coordinates of the circumscribed circle: U[0.78; 2.5111414148]
Coordinates of the inscribed circle: I[0.78; 0.67105870238]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.62769265587° = 98°37'37″ = 1.4220228054 rad
∠ B' = β' = 98.62769265587° = 98°37'37″ = 1.4220228054 rad
∠ C' = γ' = 162.7466146883° = 162°44'46″ = 0.30111365456 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 = 5.2+5.2+1.56 = 11.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.96 }{ 2 } = 5.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.98 * (5.98-5.2)(5.98-5.2)(5.98-1.56) } ; ; T = sqrt{ 16.08 } = 4.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.01 }{ 5.2 } = 1.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.01 }{ 5.2 } = 1.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.01 }{ 1.56 } = 5.14 ; ;

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{ 5.2**2+1.56**2-5.2**2 }{ 2 * 5.2 * 1.56 } ) = 81° 22'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.2**2+1.56**2-5.2**2 }{ 2 * 5.2 * 1.56 } ) = 81° 22'23" ; ; gamma = 180° - alpha - beta = 180° - 81° 22'23" - 81° 22'23" = 17° 15'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.01 }{ 5.98 } = 0.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.2 }{ 2 * sin 81° 22'23" } = 2.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 1.56**2 - 5.2**2 } }{ 2 } = 2.824 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.56**2+2 * 5.2**2 - 5.2**2 } }{ 2 } = 2.824 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 5.2**2 - 1.56**2 } }{ 2 } = 5.141 ; ;
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