Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10.3   b = 10.3   c = 14.56

Area: T = 53.0454979531
Perimeter: p = 35.16
Semiperimeter: s = 17.58

Angle ∠ A = α = 45.02551671568° = 45°1'31″ = 0.78658374131 rad
Angle ∠ B = β = 45.02551671568° = 45°1'31″ = 0.78658374131 rad
Angle ∠ C = γ = 89.95496656863° = 89°56'59″ = 1.57699178273 rad

Height: ha = 10.32999960254
Height: hb = 10.32999960254
Height: hc = 7.28663982872

Median: ma = 11.51217027411
Median: mb = 11.51217027411
Median: mc = 7.28663982872

Inradius: r = 3.01773480962
Circumradius: R = 7.28800028092

Vertex coordinates: A[14.56; 0] B[0; 0] C[7.28; 7.28663982872]
Centroid: CG[7.28; 2.42987994291]
Coordinates of the circumscribed circle: U[7.28; 0.0066395478]
Coordinates of the inscribed circle: I[7.28; 3.01773480962]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9754832843° = 134°58'29″ = 0.78658374131 rad
∠ B' = β' = 134.9754832843° = 134°58'29″ = 0.78658374131 rad
∠ C' = γ' = 90.05503343137° = 90°3'1″ = 1.57699178273 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 = 10.3+10.3+14.56 = 35.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.16 }{ 2 } = 17.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.58 * (17.58-10.3)(17.58-10.3)(17.58-14.56) } ; ; T = sqrt{ 2813.77 } = 53.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.04 }{ 10.3 } = 10.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.04 }{ 10.3 } = 10.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.04 }{ 14.56 } = 7.29 ; ;

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{ 10.3**2+14.56**2-10.3**2 }{ 2 * 10.3 * 14.56 } ) = 45° 1'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.3**2+14.56**2-10.3**2 }{ 2 * 10.3 * 14.56 } ) = 45° 1'31" ; ; gamma = 180° - alpha - beta = 180° - 45° 1'31" - 45° 1'31" = 89° 56'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.04 }{ 17.58 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.3 }{ 2 * sin 45° 1'31" } = 7.28 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.3**2+2 * 14.56**2 - 10.3**2 } }{ 2 } = 11.512 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.56**2+2 * 10.3**2 - 10.3**2 } }{ 2 } = 11.512 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.3**2+2 * 10.3**2 - 14.56**2 } }{ 2 } = 7.286 ; ;
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