15 27 28 triangle

Acute scalene triangle.

Sides: a = 15   b = 27   c = 28

Area: T = 197.9989898732
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 31.58663380965° = 31°35'11″ = 0.55112855984 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 77.8854882538° = 77°53'6″ = 1.35993476378 rad

Height: ha = 26.39986531643
Height: hb = 14.66659184246
Height: hc = 14.14221356237

Median: ma = 26.46222372448
Median: mb = 17.9511323071
Median: mc = 16.76330546142

Inradius: r = 5.65768542495
Circumradius: R = 14.3198912319

Vertex coordinates: A[28; 0] B[0; 0] C[5; 14.14221356237]
Centroid: CG[11; 4.71440452079]
Coordinates of the circumscribed circle: U[14; 3.005520382]
Coordinates of the inscribed circle: I[8; 5.65768542495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.4143661903° = 148°24'49″ = 0.55112855984 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 102.1155117462° = 102°6'54″ = 1.35993476378 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 = 27 ; ; c = 28 ; ;

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

p = a+b+c = 15+27+28 = 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 * (35-15)(35-27)(35-28) } ; ; T = sqrt{ 39200 } = 197.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.99 }{ 15 } = 26.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.99 }{ 27 } = 14.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.99 }{ 28 } = 14.14 ; ;

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**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 31° 35'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-27**2 }{ 2 * 27 * 15 } ) = 77° 53'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.99 }{ 35 } = 5.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 35'11" } = 14.32 ; ;




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