7 13 13 triangle

Acute isosceles triangle.

Sides: a = 7   b = 13   c = 13

Area: T = 43.82199440894
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 31.23769965513° = 31°14'13″ = 0.54551884383 rad
Angle ∠ B = β = 74.38215017244° = 74°22'53″ = 1.29882021077 rad
Angle ∠ C = γ = 74.38215017244° = 74°22'53″ = 1.29882021077 rad

Height: ha = 12.52199840255
Height: hb = 6.74215298599
Height: hc = 6.74215298599

Median: ma = 12.52199840255
Median: mb = 8.17700673192
Median: mc = 8.17700673192

Inradius: r = 2.65657541872
Circumradius: R = 6.74992098894

Vertex coordinates: A[13; 0] B[0; 0] C[1.88546153846; 6.74215298599]
Centroid: CG[4.96215384615; 2.247717662]
Coordinates of the circumscribed circle: U[6.5; 1.81770949702]
Coordinates of the inscribed circle: I[3.5; 2.65657541872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7633003449° = 148°45'47″ = 0.54551884383 rad
∠ B' = β' = 105.6188498276° = 105°37'7″ = 1.29882021077 rad
∠ C' = γ' = 105.6188498276° = 105°37'7″ = 1.29882021077 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 = 7 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 7+13+13 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-7)(16.5-13)(16.5-13) } ; ; T = sqrt{ 1920.19 } = 43.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.82 }{ 7 } = 12.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.82 }{ 13 } = 6.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.82 }{ 13 } = 6.74 ; ;

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{ 7**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 31° 14'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-7**2-13**2 }{ 2 * 7 * 13 } ) = 74° 22'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-7**2-13**2 }{ 2 * 13 * 7 } ) = 74° 22'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.82 }{ 16.5 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 31° 14'13" } = 6.75 ; ;




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