Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c (as equilateral triangle).

Acute isosceles triangle.

Sides: a = 66   b = 66   c = 77

Area: T = 2063.884370251
Perimeter: p = 209
Semiperimeter: s = 104.5

Angle ∠ A = α = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 71.37106694253° = 71°22'14″ = 1.24656531708 rad

Height: ha = 62.54219303792
Height: hb = 62.54219303792
Height: hc = 53.60773688964

Median: ma = 63.66771029653
Median: mb = 63.66771029653
Median: mc = 53.60773688964

Inradius: r = 19.75500832776
Circumradius: R = 40.62987427426

Vertex coordinates: A[77; 0] B[0; 0] C[38.5; 53.60773688964]
Centroid: CG[38.5; 17.86991229655]
Coordinates of the circumscribed circle: U[38.5; 12.97986261539]
Coordinates of the inscribed circle: I[38.5; 19.75500832776]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 108.6299330575° = 108°37'46″ = 1.24656531708 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c (as equilateral triangle).

a = 66 ; ; b = 66 ; ; c = 77 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 66 ; ; b = 66 ; ; c = 77 ; ; : Nr. 1

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

p = a+b+c = 66+66+77 = 209 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 209 }{ 2 } = 104.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 104.5 * (104.5-66)(104.5-66)(104.5-77) } ; ; T = sqrt{ 4259615.94 } = 2063.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2063.88 }{ 66 } = 62.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2063.88 }{ 66 } = 62.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2063.88 }{ 77 } = 53.61 ; ;

6. 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{ 66**2+77**2-66**2 }{ 2 * 66 * 77 } ) = 54° 18'53" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 66**2+77**2-66**2 }{ 2 * 66 * 77 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 66**2+66**2-77**2 }{ 2 * 66 * 66 } ) = 71° 22'14" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2063.88 }{ 104.5 } = 19.75 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 66 }{ 2 * sin 54° 18'53" } = 40.63 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 66**2+2 * 77**2 - 66**2 } }{ 2 } = 63.667 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 77**2+2 * 66**2 - 66**2 } }{ 2 } = 63.667 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 66**2+2 * 66**2 - 77**2 } }{ 2 } = 53.607 ; ;
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