130 90 66.2 triangle

Obtuse scalene triangle.

Sides: a = 130   b = 90   c = 66.2

Area: T = 2766.724436789
Perimeter: p = 286.2
Semiperimeter: s = 143.1

Angle ∠ A = α = 111.7660341514° = 111°45'37″ = 1.95105859326 rad
Angle ∠ B = β = 40.01440683351° = 40°51″ = 0.69883772396 rad
Angle ∠ C = γ = 28.2265590151° = 28°13'32″ = 0.49326294815 rad

Height: ha = 42.56549902753
Height: hb = 61.4832763731
Height: hc = 83.58768389092

Median: ma = 44.90223384692
Median: mb = 92.82435961381
Median: mc = 106.79113386

Inradius: r = 19.33442024311
Circumradius: R = 69.98770945754

Vertex coordinates: A[66.2; 0] B[0; 0] C[99.56552567976; 83.58768389092]
Centroid: CG[55.25550855992; 27.86222796364]
Coordinates of the circumscribed circle: U[33.1; 61.66550906682]
Coordinates of the inscribed circle: I[53.1; 19.33442024311]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 68.24396584861° = 68°14'23″ = 1.95105859326 rad
∠ B' = β' = 139.9865931665° = 139°59'9″ = 0.69883772396 rad
∠ C' = γ' = 151.7744409849° = 151°46'28″ = 0.49326294815 rad

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How did we calculate this triangle?

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 = 130 ; ; b = 90 ; ; c = 66.2 ; ;

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

p = a+b+c = 130+90+66.2 = 286.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 286.2 }{ 2 } = 143.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 143.1 * (143.1-130)(143.1-90)(143.1-66.2) } ; ; T = sqrt{ 7654763.73 } = 2766.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2766.72 }{ 130 } = 42.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2766.72 }{ 90 } = 61.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2766.72 }{ 66.2 } = 83.59 ; ;

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{ 90**2+66.2**2-130**2 }{ 2 * 90 * 66.2 } ) = 111° 45'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 130**2+66.2**2-90**2 }{ 2 * 130 * 66.2 } ) = 40° 51" ; ; gamma = 180° - alpha - beta = 180° - 111° 45'37" - 40° 51" = 28° 13'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2766.72 }{ 143.1 } = 19.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 130 }{ 2 * sin 111° 45'37" } = 69.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 66.2**2 - 130**2 } }{ 2 } = 44.902 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.2**2+2 * 130**2 - 90**2 } }{ 2 } = 92.824 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 130**2 - 66.2**2 } }{ 2 } = 106.791 ; ;
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