8 8 13 triangle

Obtuse isosceles triangle.

Sides: a = 8   b = 8   c = 13

Area: T = 30.31439819225
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ B = β = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ C = γ = 108.6821824608° = 108°40'55″ = 1.89768556765 rad

Height: ha = 7.57884954806
Height: hb = 7.57884954806
Height: hc = 4.66436895265

Median: ma = 10.02549688279
Median: mb = 10.02549688279
Median: mc = 4.66436895265

Inradius: r = 2.09106194429
Circumradius: R = 6.8621520223

Vertex coordinates: A[13; 0] B[0; 0] C[6.5; 4.66436895265]
Centroid: CG[6.5; 1.55545631755]
Coordinates of the circumscribed circle: U[6.5; -2.19878306964]
Coordinates of the inscribed circle: I[6.5; 2.09106194429]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ B' = β' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ C' = γ' = 71.31881753923° = 71°19'5″ = 1.89768556765 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 = 8 ; ; b = 8 ; ; c = 13 ; ;

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

p = a+b+c = 8+8+13 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-8)(14.5-8)(14.5-13) } ; ; T = sqrt{ 918.94 } = 30.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.31 }{ 8 } = 7.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.31 }{ 8 } = 7.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.31 }{ 13 } = 4.66 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 8**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 35° 39'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 35° 39'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 108° 40'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.31 }{ 14.5 } = 2.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 35° 39'33" } = 6.86 ; ;




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