6 23 28 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 28

Area: T = 41.99333030375
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 7.49435155488° = 7°29'37″ = 0.13107865189 rad
Angle ∠ B = β = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ C = γ = 142.5121758924° = 142°30'42″ = 2.4877299416 rad

Height: ha = 13.99877676792
Height: hb = 3.65215915685
Height: hc = 32.9995216455

Median: ma = 25.44660213
Median: mb = 16.66658333125
Median: mc = 9.30105376189

Inradius: r = 1.47334492294
Circumradius: R = 23.00436679691

Vertex coordinates: A[28; 0] B[0; 0] C[5.19664285714; 32.9995216455]
Centroid: CG[11.06554761905; 10.9998405485]
Coordinates of the circumscribed circle: U[14; -18.25329104537]
Coordinates of the inscribed circle: I[5.5; 1.47334492294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.5066484451° = 172°30'23″ = 0.13107865189 rad
∠ B' = β' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ C' = γ' = 37.48882410762° = 37°29'18″ = 2.4877299416 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 = 6 ; ; b = 23 ; ; c = 28 ; ;

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

p = a+b+c = 6+23+28 = 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 * (28.5-6)(28.5-23)(28.5-28) } ; ; T = sqrt{ 1763.44 } = 41.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.99 }{ 6 } = 14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.99 }{ 23 } = 3.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.99 }{ 28 } = 3 ; ;

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{ 6**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 7° 29'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-28**2 }{ 2 * 6 * 28 } ) = 29° 59'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 142° 30'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.99 }{ 28.5 } = 1.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 7° 29'37" } = 23 ; ;




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