Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 46.55   b = 46.55   c = 34.91

Area: T = 753.2454527097
Perimeter: p = 128.01
Semiperimeter: s = 64.005

Angle ∠ A = α = 67.97773468227° = 67°58'38″ = 1.18664285188 rad
Angle ∠ B = β = 67.97773468227° = 67°58'38″ = 1.18664285188 rad
Angle ∠ C = γ = 44.04553063546° = 44°2'43″ = 0.76987356159 rad

Height: ha = 32.36328153425
Height: hb = 32.36328153425
Height: hc = 43.15435105756

Median: ma = 33.92875651204
Median: mb = 33.92875651204
Median: mc = 43.15435105756

Inradius: r = 11.76985263198
Circumradius: R = 25.10769086975

Vertex coordinates: A[34.91; 0] B[0; 0] C[17.455; 43.15435105756]
Centroid: CG[17.455; 14.38545035252]
Coordinates of the circumscribed circle: U[17.455; 18.04766018781]
Coordinates of the inscribed circle: I[17.455; 11.76985263198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0232653177° = 112°1'22″ = 1.18664285188 rad
∠ B' = β' = 112.0232653177° = 112°1'22″ = 1.18664285188 rad
∠ C' = γ' = 135.9554693645° = 135°57'17″ = 0.76987356159 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 = 46.55+46.55+34.91 = 128.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 128.01 }{ 2 } = 64.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.01 * (64.01-46.55)(64.01-46.55)(64.01-34.91) } ; ; T = sqrt{ 567377.32 } = 753.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 753.24 }{ 46.55 } = 32.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 753.24 }{ 46.55 } = 32.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 753.24 }{ 34.91 } = 43.15 ; ;

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{ 46.55**2+34.91**2-46.55**2 }{ 2 * 46.55 * 34.91 } ) = 67° 58'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 46.55**2+34.91**2-46.55**2 }{ 2 * 46.55 * 34.91 } ) = 67° 58'38" ; ; gamma = 180° - alpha - beta = 180° - 67° 58'38" - 67° 58'38" = 44° 2'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 753.24 }{ 64.01 } = 11.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 46.55 }{ 2 * sin 67° 58'38" } = 25.11 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.55**2+2 * 34.91**2 - 46.55**2 } }{ 2 } = 33.928 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 34.91**2+2 * 46.55**2 - 46.55**2 } }{ 2 } = 33.928 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.55**2+2 * 46.55**2 - 34.91**2 } }{ 2 } = 43.154 ; ;
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