Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 16   b = 20   c = 20

Area: T = 146.6422422239
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: ha = 18.33303027798
Height: hb = 14.66442422239
Height: hc = 14.66442422239

Median: ma = 18.33303027798
Median: mb = 15.10996688705
Median: mc = 15.10996688705

Inradius: r = 5.23772293657
Circumradius: R = 10.91108945118

Vertex coordinates: A[20; 0] B[0; 0] C[6.4; 14.66442422239]
Centroid: CG[8.8; 4.88880807413]
Coordinates of the circumscribed circle: U[10; 4.36443578047]
Coordinates of the inscribed circle: I[8; 5.23772293657]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 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 = 16+20+20 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-16)(28-20)(28-20) } ; ; T = sqrt{ 21504 } = 146.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.64 }{ 16 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.64 }{ 20 } = 14.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.64 }{ 20 } = 14.66 ; ;

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{ 20**2+20**2-16**2 }{ 2 * 20 * 20 } ) = 47° 9'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+20**2-20**2 }{ 2 * 16 * 20 } ) = 66° 25'19" ; ;
 gamma = 180° - alpha - beta = 180° - 47° 9'23" - 66° 25'19" = 66° 25'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.64 }{ 28 } = 5.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 47° 9'23" } = 10.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 20**2 - 16**2 } }{ 2 } = 18.33 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 16**2 - 20**2 } }{ 2 } = 15.1 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 16**2 - 20**2 } }{ 2 } = 15.1 ; ;
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