Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 2.83   b = 3.16   c = 3.16

Area: T = 3.99880636575
Perimeter: p = 9.15
Semiperimeter: s = 4.575

Angle ∠ A = α = 53.20332964987° = 53°12'12″ = 0.92985726968 rad
Angle ∠ B = β = 63.39883517506° = 63°23'54″ = 1.10765099784 rad
Angle ∠ C = γ = 63.39883517506° = 63°23'54″ = 1.10765099784 rad

Height: ha = 2.82554866837
Height: hb = 2.53304200364
Height: hc = 2.53304200364

Median: ma = 2.82554866837
Median: mb = 2.55496764501
Median: mc = 2.55496764501

Inradius: r = 0.87438936956
Circumradius: R = 1.76770584076

Vertex coordinates: A[3.16; 0] B[0; 0] C[1.26772310127; 2.53304200364]
Centroid: CG[1.47657436709; 0.84334733455]
Coordinates of the circumscribed circle: U[1.58; 0.79112619135]
Coordinates of the inscribed circle: I[1.415; 0.87438936956]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.7976703501° = 126°47'48″ = 0.92985726968 rad
∠ B' = β' = 116.6021648249° = 116°36'6″ = 1.10765099784 rad
∠ C' = γ' = 116.6021648249° = 116°36'6″ = 1.10765099784 rad

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How did we calculate this triangle?

a = 2.83 ; ; b = 3.16 ; ; c = 3.16 ; ;

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

p = a+b+c = 2.83+3.16+3.16 = 9.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9.15 }{ 2 } = 4.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.58 * (4.58-2.83)(4.58-3.16)(4.58-3.16) } ; ; T = sqrt{ 15.98 } = 4 ; ;

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 }{ 2.83 } = 2.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4 }{ 3.16 } = 2.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4 }{ 3.16 } = 2.53 ; ;

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{ 3.16**2+3.16**2-2.83**2 }{ 2 * 3.16 * 3.16 } ) = 53° 12'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.83**2+3.16**2-3.16**2 }{ 2 * 2.83 * 3.16 } ) = 63° 23'54" ; ; gamma = 180° - alpha - beta = 180° - 53° 12'12" - 63° 23'54" = 63° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4 }{ 4.58 } = 0.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.83 }{ 2 * sin 53° 12'12" } = 1.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 3.16**2 - 2.83**2 } }{ 2 } = 2.825 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 2.83**2 - 3.16**2 } }{ 2 } = 2.55 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 2.83**2 - 3.16**2 } }{ 2 } = 2.55 ; ;
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