Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 21   b = 24   c = 29

Area: T = 248.1298998708
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 45.48107045498° = 45°28'51″ = 0.79437880405 rad
Angle ∠ B = β = 54.57548616063° = 54°34'29″ = 0.95325110239 rad
Angle ∠ C = γ = 79.94444338439° = 79°56'40″ = 1.39552935892 rad

Height: ha = 23.63113332103
Height: hb = 20.6777416559
Height: hc = 17.11223447385

Median: ma = 24.45991496173
Median: mb = 22.29334968096
Median: mc = 17.27699160392

Inradius: r = 6.70661891543
Circumradius: R = 14.72662110395

Vertex coordinates: A[29; 0] B[0; 0] C[12.17224137931; 17.11223447385]
Centroid: CG[13.7244137931; 5.70441149128]
Coordinates of the circumscribed circle: U[14.5; 2.57112431974]
Coordinates of the inscribed circle: I[13; 6.70661891543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.519929545° = 134°31'9″ = 0.79437880405 rad
∠ B' = β' = 125.4255138394° = 125°25'31″ = 0.95325110239 rad
∠ C' = γ' = 100.0565566156° = 100°3'20″ = 1.39552935892 rad

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How did we calculate this triangle?

a = 21 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 21+24+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-21)(37-24)(37-29) } ; ; T = sqrt{ 61568 } = 248.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 248.13 }{ 21 } = 23.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 248.13 }{ 24 } = 20.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 248.13 }{ 29 } = 17.11 ; ;

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+29**2-21**2 }{ 2 * 24 * 29 } ) = 45° 28'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 21**2+29**2-24**2 }{ 2 * 21 * 29 } ) = 54° 34'29" ; ; gamma = 180° - alpha - beta = 180° - 45° 28'51" - 54° 34'29" = 79° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 248.13 }{ 37 } = 6.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 21 }{ 2 * sin 45° 28'51" } = 14.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 29**2 - 21**2 } }{ 2 } = 24.459 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 21**2 - 24**2 } }{ 2 } = 22.293 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 21**2 - 29**2 } }{ 2 } = 17.27 ; ;
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