Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4   b = 6   c = 6

Area: T = 11.3143708499
Perimeter: p = 16
Semiperimeter: s = 8

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 5.65768542495
Height: hb = 3.77112361663
Height: hc = 3.77112361663

Median: ma = 5.65768542495
Median: mb = 4.12331056256
Median: mc = 4.12331056256

Inradius: r = 1.41442135624
Circumradius: R = 3.18219805153

Vertex coordinates: A[6; 0] B[0; 0] C[1.33333333333; 3.77112361663]
Centroid: CG[2.44444444444; 1.25770787221]
Coordinates of the circumscribed circle: U[3; 1.06106601718]
Coordinates of the inscribed circle: I[2; 1.41442135624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 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 = 4+6+6 = 16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16 }{ 2 } = 8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8 * (8-4)(8-6)(8-6) } ; ; T = sqrt{ 128 } = 11.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.31 }{ 4 } = 5.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.31 }{ 6 } = 3.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.31 }{ 6 } = 3.77 ; ;

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{ 6**2+6**2-4**2 }{ 2 * 6 * 6 } ) = 38° 56'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+6**2-6**2 }{ 2 * 4 * 6 } ) = 70° 31'44" ; ; gamma = 180° - alpha - beta = 180° - 38° 56'33" - 70° 31'44" = 70° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.31 }{ 8 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 38° 56'33" } = 3.18 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6**2 - 4**2 } }{ 2 } = 5.657 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 4**2 - 6**2 } }{ 2 } = 4.123 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 4**2 - 6**2 } }{ 2 } = 4.123 ; ;
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