7 27 27 triangle

Acute isosceles triangle.

Sides: a = 7   b = 27   c = 27

Area: T = 93.70326547116
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 14.89663811221° = 14°53'47″ = 0.26599908972 rad
Angle ∠ B = β = 82.5521809439° = 82°33'7″ = 1.44108008782 rad
Angle ∠ C = γ = 82.5521809439° = 82°33'7″ = 1.44108008782 rad

Height: ha = 26.77221870605
Height: hb = 6.9410937386
Height: hc = 6.9410937386

Median: ma = 26.77221870605
Median: mb = 14.37988038445
Median: mc = 14.37988038445

Inradius: r = 3.07222181873
Circumradius: R = 13.61548757357

Vertex coordinates: A[27; 0] B[0; 0] C[0.90774074074; 6.9410937386]
Centroid: CG[9.30224691358; 2.31436457953]
Coordinates of the circumscribed circle: U[13.5; 1.76548912991]
Coordinates of the inscribed circle: I[3.5; 3.07222181873]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1043618878° = 165°6'13″ = 0.26599908972 rad
∠ B' = β' = 97.4488190561° = 97°26'53″ = 1.44108008782 rad
∠ C' = γ' = 97.4488190561° = 97°26'53″ = 1.44108008782 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 = 27 ; ; c = 27 ; ;

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

p = a+b+c = 7+27+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-7)(30.5-27)(30.5-27) } ; ; T = sqrt{ 8780.19 } = 93.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.7 }{ 7 } = 26.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.7 }{ 27 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.7 }{ 27 } = 6.94 ; ;

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**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 14° 53'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 82° 33'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-27**2 }{ 2 * 27 * 7 } ) = 82° 33'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.7 }{ 30.5 } = 3.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 53'47" } = 13.61 ; ;




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