Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4.47   b = 4.47   c = 2.83

Area: T = 65.9997793753
Perimeter: p = 11.77
Semiperimeter: s = 5.885

Angle ∠ A = α = 71.5455298212° = 71°32'43″ = 1.24987010181 rad
Angle ∠ B = β = 71.5455298212° = 71°32'43″ = 1.24987010181 rad
Angle ∠ C = γ = 36.90994035761° = 36°54'34″ = 0.64441906173 rad

Height: ha = 2.68444650449
Height: hb = 2.68444650449
Height: hc = 4.2440126767

Median: ma = 32.9999458328
Median: mb = 32.9999458328
Median: mc = 4.2440126767

Inradius: r = 1.02195037171
Circumradius: R = 2.35661677631

Vertex coordinates: A[2.83; 0] B[0; 0] C[1.415; 4.2440126767]
Centroid: CG[1.415; 1.4133375589]
Coordinates of the circumscribed circle: U[1.415; 1.88439590038]
Coordinates of the inscribed circle: I[1.415; 1.02195037171]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4554701788° = 108°27'17″ = 1.24987010181 rad
∠ B' = β' = 108.4554701788° = 108°27'17″ = 1.24987010181 rad
∠ C' = γ' = 143.0910596424° = 143°5'26″ = 0.64441906173 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 = 4.47+4.47+2.83 = 11.77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.77 }{ 2 } = 5.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.89 * (5.89-4.47)(5.89-4.47)(5.89-2.83) } ; ; T = sqrt{ 36 } = 6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6 }{ 4.47 } = 2.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 4.47 } = 2.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 2.83 } = 4.24 ; ;

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{ 4.47**2+2.83**2-4.47**2 }{ 2 * 4.47 * 2.83 } ) = 71° 32'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.47**2+2.83**2-4.47**2 }{ 2 * 4.47 * 2.83 } ) = 71° 32'43" ; ; gamma = 180° - alpha - beta = 180° - 71° 32'43" - 71° 32'43" = 36° 54'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 5.89 } = 1.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.47 }{ 2 * sin 71° 32'43" } = 2.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 2.83**2 - 4.47**2 } }{ 2 } = 3 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.83**2+2 * 4.47**2 - 4.47**2 } }{ 2 } = 3 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 4.47**2 - 2.83**2 } }{ 2 } = 4.24 ; ;
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