Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 55.17   b = 55.17   c = 46.63

Area: T = 1165.783256477
Perimeter: p = 156.97
Semiperimeter: s = 78.485

Angle ∠ A = α = 65.00109734322° = 65°3″ = 1.13444810034 rad
Angle ∠ B = β = 65.00109734322° = 65°3″ = 1.13444810034 rad
Angle ∠ C = γ = 49.99880531355° = 49°59'53″ = 0.87326306468 rad

Height: ha = 42.26114669121
Height: hb = 42.26114669121
Height: hc = 50.00113967305

Median: ma = 42.99896577679
Median: mb = 42.99896577679
Median: mc = 50.00113967305

Inradius: r = 14.85435715713
Circumradius: R = 30.436643877

Vertex coordinates: A[46.63; 0] B[0; 0] C[23.315; 50.00113967305]
Centroid: CG[23.315; 16.66771322435]
Coordinates of the circumscribed circle: U[23.315; 19.56549579605]
Coordinates of the inscribed circle: I[23.315; 14.85435715713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9999026568° = 114°59'57″ = 1.13444810034 rad
∠ B' = β' = 114.9999026568° = 114°59'57″ = 1.13444810034 rad
∠ C' = γ' = 130.0021946864° = 130°7″ = 0.87326306468 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 = 55.17+55.17+46.63 = 156.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 156.97 }{ 2 } = 78.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 78.49 * (78.49-55.17)(78.49-55.17)(78.49-46.63) } ; ; T = sqrt{ 1359048.99 } = 1165.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1165.78 }{ 55.17 } = 42.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1165.78 }{ 55.17 } = 42.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1165.78 }{ 46.63 } = 50 ; ;

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{ 55.17**2+46.63**2-55.17**2 }{ 2 * 55.17 * 46.63 } ) = 65° 3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 55.17**2+46.63**2-55.17**2 }{ 2 * 55.17 * 46.63 } ) = 65° 3" ; ; gamma = 180° - alpha - beta = 180° - 65° 3" - 65° 3" = 49° 59'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1165.78 }{ 78.49 } = 14.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 55.17 }{ 2 * sin 65° 3" } = 30.44 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55.17**2+2 * 46.63**2 - 55.17**2 } }{ 2 } = 42.99 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.63**2+2 * 55.17**2 - 55.17**2 } }{ 2 } = 42.99 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55.17**2+2 * 55.17**2 - 46.63**2 } }{ 2 } = 50.001 ; ;
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