Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 24.19   b = 25.5   c = 8.06

Area: T = 97.48656945575
Perimeter: p = 57.75
Semiperimeter: s = 28.875

Angle ∠ A = α = 71.5554925605° = 71°33'18″ = 1.24988690478 rad
Angle ∠ B = β = 90.01991454752° = 90°1'9″ = 1.57111304784 rad
Angle ∠ C = γ = 18.42659289198° = 18°25'33″ = 0.32215931274 rad

Height: ha = 8.065999955
Height: hb = 7.6465936828
Height: hc = 24.19899986495

Median: ma = 14.53767731977
Median: mb = 12.7477444842
Median: mc = 24.52547252788

Inradius: r = 3.376612795
Circumradius: R = 12.75500007118

Vertex coordinates: A[8.06; 0] B[0; 0] C[-0.00880831266; 24.19899986495]
Centroid: CG[2.68439722911; 8.06333328832]
Coordinates of the circumscribed circle: U[4.03; 12.09663473062]
Coordinates of the inscribed circle: I[3.375; 3.376612795]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4455074395° = 108°26'42″ = 1.24988690478 rad
∠ B' = β' = 89.98108545248° = 89°58'51″ = 1.57111304784 rad
∠ C' = γ' = 161.574407108° = 161°34'27″ = 0.32215931274 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 = 24.19+25.5+8.06 = 57.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57.75 }{ 2 } = 28.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.88 * (28.88-24.19)(28.88-25.5)(28.88-8.06) } ; ; T = sqrt{ 9503.46 } = 97.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.49 }{ 24.19 } = 8.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.49 }{ 25.5 } = 7.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.49 }{ 8.06 } = 24.19 ; ;

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{ 25.5**2+8.06**2-24.19**2 }{ 2 * 25.5 * 8.06 } ) = 71° 33'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.19**2+8.06**2-25.5**2 }{ 2 * 24.19 * 8.06 } ) = 90° 1'9" ; ;
 gamma = 180° - alpha - beta = 180° - 71° 33'18" - 90° 1'9" = 18° 25'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.49 }{ 28.88 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.19 }{ 2 * sin 71° 33'18" } = 12.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.5**2+2 * 8.06**2 - 24.19**2 } }{ 2 } = 14.537 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 24.19**2 - 25.5**2 } }{ 2 } = 12.747 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.5**2+2 * 24.19**2 - 8.06**2 } }{ 2 } = 24.525 ; ;
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