Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 20   b = 24   c = 26

Area: T = 227.9880262304
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 46.94656106092° = 46°56'44″ = 0.81993554745 rad
Angle ∠ B = β = 61.26443462551° = 61°15'52″ = 1.06992645562 rad
Angle ∠ C = γ = 71.79900431357° = 71°47'24″ = 1.25329726229 rad

Height: ha = 22.79880262304
Height: hb = 18.9988355192
Height: hc = 17.53769432541

Median: ma = 22.93546898824
Median: mb = 19.84994332413
Median: mc = 17.86105710995

Inradius: r = 6.51437217801
Circumradius: R = 13.68553952552

Vertex coordinates: A[26; 0] B[0; 0] C[9.61553846154; 17.53769432541]
Centroid: CG[11.87217948718; 5.84656477514]
Coordinates of the circumscribed circle: U[13; 4.27766860172]
Coordinates of the inscribed circle: I[11; 6.51437217801]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.0544389391° = 133°3'16″ = 0.81993554745 rad
∠ B' = β' = 118.7365653745° = 118°44'8″ = 1.06992645562 rad
∠ C' = γ' = 108.2109956864° = 108°12'36″ = 1.25329726229 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+24+26 = 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)(35-24)(35-26) } ; ; T = sqrt{ 51975 } = 227.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 227.98 }{ 20 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 227.98 }{ 24 } = 19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 227.98 }{ 26 } = 17.54 ; ;

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{ 24**2+26**2-20**2 }{ 2 * 24 * 26 } ) = 46° 56'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+26**2-24**2 }{ 2 * 20 * 26 } ) = 61° 15'52" ; ;
 gamma = 180° - alpha - beta = 180° - 46° 56'44" - 61° 15'52" = 71° 47'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 227.98 }{ 35 } = 6.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 46° 56'44" } = 13.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 26**2 - 20**2 } }{ 2 } = 22.935 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 20**2 - 24**2 } }{ 2 } = 19.849 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 20**2 - 26**2 } }{ 2 } = 17.861 ; ;
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