Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 20   b = 25   c = 25

Area: T = 229.1298784748
Perimeter: p = 70
Semiperimeter: s = 35

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 = 22.91328784748
Height: hb = 18.33303027798
Height: hc = 18.33303027798

Median: ma = 22.91328784748
Median: mb = 18.87545860882
Median: mc = 18.87545860882

Inradius: r = 6.54765367071
Circumradius: R = 13.63986181397

Vertex coordinates: A[25; 0] B[0; 0] C[8; 18.33303027798]
Centroid: CG[11; 6.11101009266]
Coordinates of the circumscribed circle: U[12.5; 5.45554472559]
Coordinates of the inscribed circle: I[10; 6.54765367071]

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 = 20+25+25 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-20)(35-25)(35-25) } ; ; T = sqrt{ 52500 } = 229.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 229.13 }{ 20 } = 22.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 229.13 }{ 25 } = 18.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 229.13 }{ 25 } = 18.33 ; ;

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{ 25**2+25**2-20**2 }{ 2 * 25 * 25 } ) = 47° 9'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+25**2-25**2 }{ 2 * 20 * 25 } ) = 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{ 229.13 }{ 35 } = 6.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 47° 9'23" } = 13.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 25**2 - 20**2 } }{ 2 } = 22.913 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 20**2 - 25**2 } }{ 2 } = 18.875 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 20**2 - 25**2 } }{ 2 } = 18.875 ; ;
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