Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 400   b = 400   c = 565.69

Area: T = 800009.9999895
Perimeter: p = 1365.69
Semiperimeter: s = 682.845

Angle ∠ A = α = 454.9995366114° = 44°59'58″ = 0.78553900757 rad
Angle ∠ B = β = 454.9995366114° = 44°59'58″ = 0.78553900757 rad
Angle ∠ C = γ = 90.00109267771° = 90°3″ = 1.57108125021 rad

Height: ha = 4009.999999948
Height: hb = 4009.999999948
Height: hc = 282.8440424931

Median: ma = 447.2166489018
Median: mb = 447.2166489018
Median: mc = 282.8440424931

Inradius: r = 117.1576895034
Circumradius: R = 282.8455000037

Vertex coordinates: A[565.69; 0] B[0; 0] C[282.845; 282.8440424931]
Centroid: CG[282.845; 94.28801416436]
Coordinates of the circumscribed circle: U[282.845; -0.00545751063]
Coordinates of the inscribed circle: I[282.845; 117.1576895034]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1355.000463389° = 135°2″ = 0.78553900757 rad
∠ B' = β' = 1355.000463389° = 135°2″ = 0.78553900757 rad
∠ C' = γ' = 89.99990732229° = 89°59'57″ = 1.57108125021 rad

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How did we calculate this triangle?

a = 400 ; ; b = 400 ; ; c = 565.69 ; ;

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

p = a+b+c = 400+400+565.69 = 1365.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1365.69 }{ 2 } = 682.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 682.85 * (682.85-400)(682.85-400)(682.85-565.69) } ; ; T = sqrt{ 6399999998.33 } = 80000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 80000 }{ 400 } = 400 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 80000 }{ 400 } = 400 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 80000 }{ 565.69 } = 282.84 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 400**2-400**2-565.69**2 }{ 2 * 400 * 565.69 } ) = 44° 59'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 400**2-400**2-565.69**2 }{ 2 * 400 * 565.69 } ) = 44° 59'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 565.69**2-400**2-400**2 }{ 2 * 400 * 400 } ) = 90° 3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 80000 }{ 682.85 } = 117.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 400 }{ 2 * sin 44° 59'58" } = 282.85 ; ;




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