Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 5.5   b = 5.5   c = 8.04

Area: T = 15.09895186086
Perimeter: p = 19.04
Semiperimeter: s = 9.52

Angle ∠ A = α = 43.03773394163° = 43°2'14″ = 0.75111432741 rad
Angle ∠ B = β = 43.03773394163° = 43°2'14″ = 0.75111432741 rad
Angle ∠ C = γ = 93.92553211675° = 93°55'31″ = 1.63993061054 rad

Height: ha = 5.48770976759
Height: hb = 5.48770976759
Height: hc = 3.75436115942

Median: ma = 6.31553226363
Median: mb = 6.31553226363
Median: mc = 3.75436115942

Inradius: r = 1.58550334673
Circumradius: R = 4.02994526006

Vertex coordinates: A[8.04; 0] B[0; 0] C[4.02; 3.75436115942]
Centroid: CG[4.02; 1.25112038647]
Coordinates of the circumscribed circle: U[4.02; -0.27658410065]
Coordinates of the inscribed circle: I[4.02; 1.58550334673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9632660584° = 136°57'46″ = 0.75111432741 rad
∠ B' = β' = 136.9632660584° = 136°57'46″ = 0.75111432741 rad
∠ C' = γ' = 86.07546788325° = 86°4'29″ = 1.63993061054 rad

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How did we calculate this triangle?

a = 5.5 ; ; b = 5.5 ; ; c = 8.04 ; ;

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

p = a+b+c = 5.5+5.5+8.04 = 19.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.04 }{ 2 } = 9.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.52 * (9.52-5.5)(9.52-5.5)(9.52-8.04) } ; ; T = sqrt{ 227.69 } = 15.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.09 }{ 5.5 } = 5.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.09 }{ 5.5 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.09 }{ 8.04 } = 3.75 ; ;

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{ 5.5**2+8.04**2-5.5**2 }{ 2 * 5.5 * 8.04 } ) = 43° 2'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.5**2+8.04**2-5.5**2 }{ 2 * 5.5 * 8.04 } ) = 43° 2'14" ; ; gamma = 180° - alpha - beta = 180° - 43° 2'14" - 43° 2'14" = 93° 55'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.09 }{ 9.52 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.5 }{ 2 * sin 43° 2'14" } = 4.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.5**2+2 * 8.04**2 - 5.5**2 } }{ 2 } = 6.315 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.04**2+2 * 5.5**2 - 5.5**2 } }{ 2 } = 6.315 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.5**2+2 * 5.5**2 - 8.04**2 } }{ 2 } = 3.754 ; ;
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