Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 8.6   b = 12.17   c = 8.6

Area: T = 36.98799698458
Perimeter: p = 29.37
Semiperimeter: s = 14.685

Angle ∠ A = α = 44.96334154418° = 44°57'48″ = 0.78547596424 rad
Angle ∠ B = β = 90.07331691164° = 90°4'23″ = 1.57220733688 rad
Angle ∠ C = γ = 44.96334154418° = 44°57'48″ = 0.78547596424 rad

Height: ha = 8.65999929874
Height: hb = 6.07772341571
Height: hc = 8.65999929874

Median: ma = 9.62200025988
Median: mb = 6.07772341571
Median: mc = 9.62200025988

Inradius: r = 2.51882138131
Circumradius: R = 6.08550049618

Vertex coordinates: A[8.6; 0] B[0; 0] C[-0.01109825581; 8.65999929874]
Centroid: CG[2.8633005814; 2.86766643291]
Coordinates of the circumscribed circle: U[4.3; 4.30554947898]
Coordinates of the inscribed circle: I[2.515; 2.51882138131]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0376584558° = 135°2'12″ = 0.78547596424 rad
∠ B' = β' = 89.92768308836° = 89°55'37″ = 1.57220733688 rad
∠ C' = γ' = 135.0376584558° = 135°2'12″ = 0.78547596424 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 = 8.6+12.17+8.6 = 29.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.37 }{ 2 } = 14.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.69 * (14.69-8.6)(14.69-12.17)(14.69-8.6) } ; ; T = sqrt{ 1367.52 } = 36.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.98 }{ 8.6 } = 8.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.98 }{ 12.17 } = 6.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.98 }{ 8.6 } = 8.6 ; ;

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{ 12.17**2+8.6**2-8.6**2 }{ 2 * 12.17 * 8.6 } ) = 44° 57'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.6**2+8.6**2-12.17**2 }{ 2 * 8.6 * 8.6 } ) = 90° 4'23" ; ; gamma = 180° - alpha - beta = 180° - 44° 57'48" - 90° 4'23" = 44° 57'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.98 }{ 14.69 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.6 }{ 2 * sin 44° 57'48" } = 6.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.17**2+2 * 8.6**2 - 8.6**2 } }{ 2 } = 9.62 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.6**2+2 * 8.6**2 - 12.17**2 } }{ 2 } = 6.077 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.17**2+2 * 8.6**2 - 8.6**2 } }{ 2 } = 9.62 ; ;
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