Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 58   b = 58   c = 52.66

Area: T = 1360.711114197
Perimeter: p = 168.66
Semiperimeter: s = 84.33

Angle ∠ A = α = 63.0021606477° = 63°6″ = 1.10995854671 rad
Angle ∠ B = β = 63.0021606477° = 63°6″ = 1.10995854671 rad
Angle ∠ C = γ = 53.9976787046° = 53°59'48″ = 0.94224217195 rad

Height: ha = 46.92110738612
Height: hb = 46.92110738612
Height: hc = 51.6799116672

Median: ma = 47.19767986202
Median: mb = 47.19767986202
Median: mc = 51.6799116672

Inradius: r = 16.13655524958
Circumradius: R = 32.54769959302

Vertex coordinates: A[52.66; 0] B[0; 0] C[26.33; 51.6799116672]
Centroid: CG[26.33; 17.2266372224]
Coordinates of the circumscribed circle: U[26.33; 19.13221207418]
Coordinates of the inscribed circle: I[26.33; 16.13655524958]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.9988393523° = 116°59'54″ = 1.10995854671 rad
∠ B' = β' = 116.9988393523° = 116°59'54″ = 1.10995854671 rad
∠ C' = γ' = 126.0033212954° = 126°12″ = 0.94224217195 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 = 58+58+52.66 = 168.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 168.66 }{ 2 } = 84.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.33 * (84.33-58)(84.33-58)(84.33-52.66) } ; ; T = sqrt{ 1851534.81 } = 1360.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1360.71 }{ 58 } = 46.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1360.71 }{ 58 } = 46.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1360.71 }{ 52.66 } = 51.68 ; ;

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{ 58**2+52.66**2-58**2 }{ 2 * 58 * 52.66 } ) = 63° 6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 58**2+52.66**2-58**2 }{ 2 * 58 * 52.66 } ) = 63° 6" ; ;
 gamma = 180° - alpha - beta = 180° - 63° 6" - 63° 6" = 53° 59'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1360.71 }{ 84.33 } = 16.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 58 }{ 2 * sin 63° 6" } = 32.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 58**2+2 * 52.66**2 - 58**2 } }{ 2 } = 47.197 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 52.66**2+2 * 58**2 - 58**2 } }{ 2 } = 47.197 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 58**2+2 * 58**2 - 52.66**2 } }{ 2 } = 51.679 ; ;
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