Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 13.42   b = 28.02   c = 24.6

Area: T = 165.0665996498
Perimeter: p = 66.04
Semiperimeter: s = 33.02

Angle ∠ A = α = 28.61664296738° = 28°36'59″ = 0.4999450918 rad
Angle ∠ B = β = 89.98881983175° = 89°59'18″ = 1.57105903486 rad
Angle ∠ C = γ = 61.39553720086° = 61°23'43″ = 1.0721551387 rad

Height: ha = 24.65999994781
Height: hb = 11.7822012598
Height: hc = 13.42199997153

Median: ma = 25.49773743746
Median: mb = 14.01224266278
Median: mc = 18.20221537187

Inradius: r = 4.9998970215
Circumradius: R = 14.01100002972

Vertex coordinates: A[24.6; 0] B[0; 0] C[0.00327642276; 13.42199997153]
Centroid: CG[8.20109214092; 4.47333332384]
Coordinates of the circumscribed circle: U[12.3; 6.70774666102]
Coordinates of the inscribed circle: I[5; 4.9998970215]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3843570326° = 151°23'1″ = 0.4999450918 rad
∠ B' = β' = 90.01218016825° = 90°42″ = 1.57105903486 rad
∠ C' = γ' = 118.6054627991° = 118°36'17″ = 1.0721551387 rad

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How did we calculate this triangle?

a = 13.42 ; ; b = 28.02 ; ; c = 24.6 ; ;

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

p = a+b+c = 13.42+28.02+24.6 = 66.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66.04 }{ 2 } = 33.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.02 * (33.02-13.42)(33.02-28.02)(33.02-24.6) } ; ; T = sqrt{ 27246.78 } = 165.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 165.07 }{ 13.42 } = 24.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 165.07 }{ 28.02 } = 11.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 165.07 }{ 24.6 } = 13.42 ; ;

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{ 28.02**2+24.6**2-13.42**2 }{ 2 * 28.02 * 24.6 } ) = 28° 36'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.42**2+24.6**2-28.02**2 }{ 2 * 13.42 * 24.6 } ) = 89° 59'18" ; ; gamma = 180° - alpha - beta = 180° - 28° 36'59" - 89° 59'18" = 61° 23'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 165.07 }{ 33.02 } = 5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.42 }{ 2 * sin 28° 36'59" } = 14.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.02**2+2 * 24.6**2 - 13.42**2 } }{ 2 } = 25.497 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24.6**2+2 * 13.42**2 - 28.02**2 } }{ 2 } = 14.012 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.02**2+2 * 13.42**2 - 24.6**2 } }{ 2 } = 18.202 ; ;
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