1.3 1.3 0.6 triangle

Acute isosceles triangle.

Sides: a = 1.3   b = 1.3   c = 0.6

Area: T = 0.37994733192
Perimeter: p = 3.2
Semiperimeter: s = 1.6

Angle ∠ A = α = 76.65876362029° = 76°39'28″ = 1.33879281485 rad
Angle ∠ B = β = 76.65876362029° = 76°39'28″ = 1.33879281485 rad
Angle ∠ C = γ = 26.68547275942° = 26°41'5″ = 0.46657363565 rad

Height: ha = 0.58438051065
Height: hb = 0.58438051065
Height: hc = 1.26549110641

Median: ma = 0.77662087348
Median: mb = 0.77662087348
Median: mc = 1.26549110641

Inradius: r = 0.23771708245
Circumradius: R = 0.66880311557

Vertex coordinates: A[0.6; 0] B[0; 0] C[0.3; 1.26549110641]
Centroid: CG[0.3; 0.42216370214]
Coordinates of the circumscribed circle: U[0.3; 0.59768799084]
Coordinates of the inscribed circle: I[0.3; 0.23771708245]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.3422363797° = 103°20'32″ = 1.33879281485 rad
∠ B' = β' = 103.3422363797° = 103°20'32″ = 1.33879281485 rad
∠ C' = γ' = 153.3155272406° = 153°18'55″ = 0.46657363565 rad

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How did we calculate this triangle?

a = 1.3 ; ; b = 1.3 ; ; c = 0.6 ; ;

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

p = a+b+c = 1.3+1.3+0.6 = 3.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.2 }{ 2 } = 1.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.6 * (1.6-1.3)(1.6-1.3)(1.6-0.6) } ; ; T = sqrt{ 0.14 } = 0.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.38 }{ 1.3 } = 0.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.38 }{ 1.3 } = 0.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.38 }{ 0.6 } = 1.26 ; ;

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{ 1.3**2-1.3**2-0.6**2 }{ 2 * 1.3 * 0.6 } ) = 76° 39'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.3**2-1.3**2-0.6**2 }{ 2 * 1.3 * 0.6 } ) = 76° 39'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.6**2-1.3**2-1.3**2 }{ 2 * 1.3 * 1.3 } ) = 26° 41'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.38 }{ 1.6 } = 0.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.3 }{ 2 * sin 76° 39'28" } = 0.67 ; ;




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