Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 48   b = 33.94   c = 33.94

Area: T = 575.9621798733
Perimeter: p = 115.88
Semiperimeter: s = 57.94

Angle ∠ A = α = 90.00438000763° = 90°14″ = 1.57108626506 rad
Angle ∠ B = β = 44.99880999619° = 44°59'53″ = 0.78553650015 rad
Angle ∠ C = γ = 44.99880999619° = 44°59'53″ = 0.78553650015 rad

Height: ha = 23.99884082806
Height: hb = 33.94399999254
Height: hc = 33.94399999254

Median: ma = 23.99884082806
Median: mb = 37.94770802566
Median: mc = 37.94770802566

Inradius: r = 9.94106592809
Circumradius: R = 244.0000000528

Vertex coordinates: A[33.94; 0] B[0; 0] C[33.94222510312; 33.94399999254]
Centroid: CG[22.62774170104; 11.31333333085]
Coordinates of the circumscribed circle: U[16.97; 16.97111255529]
Coordinates of the inscribed circle: I[24; 9.94106592809]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99661999237° = 89°59'46″ = 1.57108626506 rad
∠ B' = β' = 135.0021900038° = 135°7″ = 0.78553650015 rad
∠ C' = γ' = 135.0021900038° = 135°7″ = 0.78553650015 rad

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How did we calculate this triangle?

a = 48 ; ; b = 33.94 ; ; c = 33.94 ; ;

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

p = a+b+c = 48+33.94+33.94 = 115.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 115.88 }{ 2 } = 57.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.94 * (57.94-48)(57.94-33.94)(57.94-33.94) } ; ; T = sqrt{ 331731.99 } = 575.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 575.96 }{ 48 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 575.96 }{ 33.94 } = 33.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 575.96 }{ 33.94 } = 33.94 ; ;

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{ 33.94**2+33.94**2-48**2 }{ 2 * 33.94 * 33.94 } ) = 90° 14" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 48**2+33.94**2-33.94**2 }{ 2 * 48 * 33.94 } ) = 44° 59'53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 48**2+33.94**2-33.94**2 }{ 2 * 48 * 33.94 } ) = 44° 59'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 575.96 }{ 57.94 } = 9.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48 }{ 2 * sin 90° 14" } = 24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.94**2+2 * 33.94**2 - 48**2 } }{ 2 } = 23.998 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.94**2+2 * 48**2 - 33.94**2 } }{ 2 } = 37.947 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.94**2+2 * 48**2 - 33.94**2 } }{ 2 } = 37.947 ; ;
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