Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 5.66   b = 5.1   c = 5.1

Area: T = 12.00770400095
Perimeter: p = 15.86
Semiperimeter: s = 7.93

Angle ∠ A = α = 67.40879246999° = 67°24'29″ = 1.17664902279 rad
Angle ∠ B = β = 56.29660376501° = 56°17'46″ = 0.98325512128 rad
Angle ∠ C = γ = 56.29660376501° = 56°17'46″ = 0.98325512128 rad

Height: ha = 4.24327703214
Height: hb = 4.7098643141
Height: hc = 4.7098643141

Median: ma = 4.24327703214
Median: mb = 4.74655558157
Median: mc = 4.74655558157

Inradius: r = 1.51441286267
Circumradius: R = 3.06552142386

Vertex coordinates: A[5.1; 0] B[0; 0] C[3.1410745098; 4.7098643141]
Centroid: CG[2.74769150327; 1.57695477137]
Coordinates of the circumscribed circle: U[2.55; 1.70108933912]
Coordinates of the inscribed circle: I[2.83; 1.51441286267]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.59220753° = 112°35'31″ = 1.17664902279 rad
∠ B' = β' = 123.704396235° = 123°42'14″ = 0.98325512128 rad
∠ C' = γ' = 123.704396235° = 123°42'14″ = 0.98325512128 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 = 5.66+5.1+5.1 = 15.86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.86 }{ 2 } = 7.93 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.93 * (7.93-5.66)(7.93-5.1)(7.93-5.1) } ; ; T = sqrt{ 144.17 } = 12.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.01 }{ 5.66 } = 4.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.01 }{ 5.1 } = 4.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.01 }{ 5.1 } = 4.71 ; ;

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{ 5.1**2+5.1**2-5.66**2 }{ 2 * 5.1 * 5.1 } ) = 67° 24'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.66**2+5.1**2-5.1**2 }{ 2 * 5.66 * 5.1 } ) = 56° 17'46" ; ; gamma = 180° - alpha - beta = 180° - 67° 24'29" - 56° 17'46" = 56° 17'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.01 }{ 7.93 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.66 }{ 2 * sin 67° 24'29" } = 3.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 5.1**2 - 5.66**2 } }{ 2 } = 4.243 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 5.66**2 - 5.1**2 } }{ 2 } = 4.746 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 5.66**2 - 5.1**2 } }{ 2 } = 4.746 ; ;
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