15 15 27 triangle

Obtuse isosceles triangle.

Sides: a = 15   b = 15   c = 27

Area: T = 88.26877036067
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ C = γ = 128.3166134474° = 128°18'58″ = 2.243953903 rad

Height: ha = 11.76990271476
Height: hb = 11.76990271476
Height: hc = 6.53883484153

Median: ma = 20.51221914968
Median: mb = 20.51221914968
Median: mc = 6.53883484153

Inradius: r = 3.09771124073
Circumradius: R = 17.20661800403

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 6.53883484153]
Centroid: CG[13.5; 2.17994494718]
Coordinates of the circumscribed circle: U[13.5; -10.6687831625]
Coordinates of the inscribed circle: I[13.5; 3.09771124073]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ C' = γ' = 51.68438655263° = 51°41'2″ = 2.243953903 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 = 15 ; ; b = 15 ; ; c = 27 ; ;

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

p = a+b+c = 15+15+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-15)(28.5-15)(28.5-27) } ; ; T = sqrt{ 7791.19 } = 88.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.27 }{ 15 } = 11.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.27 }{ 15 } = 11.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.27 }{ 27 } = 6.54 ; ;

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{ 15**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 25° 50'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 128° 18'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.27 }{ 28.5 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 25° 50'31" } = 17.21 ; ;




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