Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 567.13   b = 575.88   c = 100

Area: T = 28356.5499998
Perimeter: p = 1243.01
Semiperimeter: s = 621.505

Angle ∠ A = α = 79.99993761607° = 79°59'58″ = 1.39662525135 rad
Angle ∠ B = β = 90.0010675622° = 90°2″ = 1.57108081186 rad
Angle ∠ C = γ = 10.9999482172° = 10° = 0.17545320214 rad

Height: ha = 100.999999993
Height: hb = 98.48105862264
Height: hc = 567.1329999961

Median: ma = 300.6822187658
Median: mb = 287.9398838731
Median: mc = 569.3330401129

Inradius: r = 45.62655380054
Circumradius: R = 287.944000002

Vertex coordinates: A[100; 0] B[0; 0] C[-0.00766875; 567.1329999961]
Centroid: CG[33.33111041667; 189.043333332]
Coordinates of the circumscribed circle: U[50; 283.5665589611]
Coordinates of the inscribed circle: I[45.625; 45.62655380054]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.0010623839° = 100°2″ = 1.39662525135 rad
∠ B' = β' = 89.9999324378° = 89°59'58″ = 1.57108081186 rad
∠ C' = γ' = 1700.000051783° = 170° = 0.17545320214 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 = 567.13+575.88+100 = 1243.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1243.01 }{ 2 } = 621.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 621.51 * (621.51-567.13)(621.51-575.88)(621.51-100) } ; ; T = sqrt{ 804091092.14 } = 28356.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28356.5 }{ 567.13 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28356.5 }{ 575.88 } = 98.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28356.5 }{ 100 } = 567.13 ; ;

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{ 575.88**2+100**2-567.13**2 }{ 2 * 575.88 * 100 } ) = 79° 59'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 567.13**2+100**2-575.88**2 }{ 2 * 567.13 * 100 } ) = 90° 2" ; ;
 gamma = 180° - alpha - beta = 180° - 79° 59'58" - 90° 2" = 10° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28356.5 }{ 621.51 } = 45.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 567.13 }{ 2 * sin 79° 59'58" } = 287.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 575.88**2+2 * 100**2 - 567.13**2 } }{ 2 } = 300.682 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 567.13**2 - 575.88**2 } }{ 2 } = 287.939 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 575.88**2+2 * 567.13**2 - 100**2 } }{ 2 } = 569.33 ; ;
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