16 27 27 triangle

Acute isosceles triangle.

Sides: a = 16   b = 27   c = 27

Area: T = 206.3010751332
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 34.47105705142° = 34°28'14″ = 0.60216249505 rad
Angle ∠ B = β = 72.76547147429° = 72°45'53″ = 1.27699838515 rad
Angle ∠ C = γ = 72.76547147429° = 72°45'53″ = 1.27699838515 rad

Height: ha = 25.78875939165
Height: hb = 15.28215371357
Height: hc = 15.28215371357

Median: ma = 25.78875939165
Median: mb = 17.61439149538
Median: mc = 17.61439149538

Inradius: r = 5.89443071809
Circumradius: R = 14.13547037332

Vertex coordinates: A[27; 0] B[0; 0] C[4.74107407407; 15.28215371357]
Centroid: CG[10.58802469136; 5.09438457119]
Coordinates of the circumscribed circle: U[13.5; 4.18880603654]
Coordinates of the inscribed circle: I[8; 5.89443071809]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5299429486° = 145°31'46″ = 0.60216249505 rad
∠ B' = β' = 107.2355285257° = 107°14'7″ = 1.27699838515 rad
∠ C' = γ' = 107.2355285257° = 107°14'7″ = 1.27699838515 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 = 16 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 16+27+27 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-16)(35-27)(35-27) } ; ; T = sqrt{ 42560 } = 206.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 206.3 }{ 16 } = 25.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 206.3 }{ 27 } = 15.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 206.3 }{ 27 } = 15.28 ; ;

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{ 16**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 34° 28'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 72° 45'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-27**2 }{ 2 * 27 * 16 } ) = 72° 45'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 206.3 }{ 35 } = 5.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 28'14" } = 14.13 ; ;




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