1 27 27 triangle

Acute isosceles triangle.

Sides: a = 1   b = 27   c = 27

Area: T = 13.49876849867
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 2.12221872153° = 2°7'20″ = 0.03770391542 rad
Angle ∠ B = β = 88.93989063924° = 88°56'20″ = 1.55222767497 rad
Angle ∠ C = γ = 88.93989063924° = 88°56'20″ = 1.55222767497 rad

Height: ha = 26.99553699734
Height: hb = 10.9998285175
Height: hc = 10.9998285175

Median: ma = 26.99553699734
Median: mb = 13.51985058346
Median: mc = 13.51985058346

Inradius: r = 0.49108249086
Circumradius: R = 13.50223154104

Vertex coordinates: A[27; 0] B[0; 0] C[0.01985185185; 10.9998285175]
Centroid: CG[9.00661728395; 0.33332761725]
Coordinates of the circumscribed circle: U[13.5; 0.2550042878]
Coordinates of the inscribed circle: I[0.5; 0.49108249086]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.8787812785° = 177°52'40″ = 0.03770391542 rad
∠ B' = β' = 91.06110936076° = 91°3'40″ = 1.55222767497 rad
∠ C' = γ' = 91.06110936076° = 91°3'40″ = 1.55222767497 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 = 1 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 1+27+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-1)(27.5-27)(27.5-27) } ; ; T = sqrt{ 182.19 } = 13.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.5 }{ 1 } = 27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.5 }{ 27 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.5 }{ 27 } = 1 ; ;

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{ 27**2+27**2-1**2 }{ 2 * 27 * 27 } ) = 2° 7'20" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1**2+27**2-27**2 }{ 2 * 1 * 27 } ) = 88° 56'20" ; ; gamma = 180° - alpha - beta = 180° - 2° 7'20" - 88° 56'20" = 88° 56'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.5 }{ 27.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1 }{ 2 * sin 2° 7'20" } = 13.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 27**2 - 1**2 } }{ 2 } = 26.995 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 1**2 - 27**2 } }{ 2 } = 13.519 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 1**2 - 27**2 } }{ 2 } = 13.519 ; ;
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