12 18 28 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 18   c = 28

Area: T = 73.64110211771
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 16.9911286937° = 16°59'29″ = 0.29765539012 rad
Angle ∠ B = β = 25.99879769925° = 25°59'53″ = 0.45437502974 rad
Angle ∠ C = γ = 137.0110736071° = 137°39″ = 2.3911288455 rad

Height: ha = 12.27435035295
Height: hb = 8.18223356863
Height: hc = 5.26600729412

Median: ma = 22.76596133535
Median: mb = 19.57703857908
Median: mc = 6.1644414003

Inradius: r = 2.53993455578
Circumradius: R = 20.53220346708

Vertex coordinates: A[28; 0] B[0; 0] C[10.78657142857; 5.26600729412]
Centroid: CG[12.92985714286; 1.75333576471]
Coordinates of the circumscribed circle: U[14; -15.01988031388]
Coordinates of the inscribed circle: I[11; 2.53993455578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0098713063° = 163°31″ = 0.29765539012 rad
∠ B' = β' = 154.0022023008° = 154°7″ = 0.45437502974 rad
∠ C' = γ' = 42.98992639295° = 42°59'21″ = 2.3911288455 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 = 12 ; ; b = 18 ; ; c = 28 ; ;

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

p = a+b+c = 12+18+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-12)(29-18)(29-28) } ; ; T = sqrt{ 5423 } = 73.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.64 }{ 12 } = 12.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.64 }{ 18 } = 8.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.64 }{ 28 } = 5.26 ; ;

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{ 12**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 16° 59'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-12**2-28**2 }{ 2 * 12 * 28 } ) = 25° 59'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-12**2-18**2 }{ 2 * 18 * 12 } ) = 137° 39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.64 }{ 29 } = 2.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 16° 59'29" } = 20.53 ; ;




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