Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 19   b = 23   c = 29

Area: T = 218.1566337291
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 40.85546193501° = 40°51'17″ = 0.71330476223 rad
Angle ∠ B = β = 52.35993005849° = 52°21'33″ = 0.91438421892 rad
Angle ∠ C = γ = 86.7866080065° = 86°47'10″ = 1.5154702842 rad

Height: ha = 22.96438249779
Height: hb = 18.97701162861
Height: hc = 15.04552646407

Median: ma = 24.38774967965
Median: mb = 21.65106350946
Median: mc = 15.3221553446

Inradius: r = 6.14552489378
Circumradius: R = 14.52328419186

Vertex coordinates: A[29; 0] B[0; 0] C[11.60334482759; 15.04552646407]
Centroid: CG[13.53444827586; 5.01550882136]
Coordinates of the circumscribed circle: U[14.5; 0.81442096728]
Coordinates of the inscribed circle: I[12.5; 6.14552489378]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.145538065° = 139°8'43″ = 0.71330476223 rad
∠ B' = β' = 127.6410699415° = 127°38'27″ = 0.91438421892 rad
∠ C' = γ' = 93.2143919935° = 93°12'50″ = 1.5154702842 rad

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How did we calculate this triangle?

a = 19 ; ; b = 23 ; ; c = 29 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 19+23+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-19)(35.5-23)(35.5-29) } ; ; T = sqrt{ 47592.19 } = 218.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218.16 }{ 19 } = 22.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218.16 }{ 23 } = 18.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218.16 }{ 29 } = 15.05 ; ;

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{ 23**2+29**2-19**2 }{ 2 * 23 * 29 } ) = 40° 51'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19**2+29**2-23**2 }{ 2 * 19 * 29 } ) = 52° 21'33" ; ; gamma = 180° - alpha - beta = 180° - 40° 51'17" - 52° 21'33" = 86° 47'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218.16 }{ 35.5 } = 6.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 19 }{ 2 * sin 40° 51'17" } = 14.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 29**2 - 19**2 } }{ 2 } = 24.387 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 19**2 - 23**2 } }{ 2 } = 21.651 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 19**2 - 29**2 } }{ 2 } = 15.322 ; ;
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