13 28 30 triangle

Acute scalene triangle.

Sides: a = 13   b = 28   c = 30

Area: T = 181.5177044654
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 25.60662067164° = 25°36'22″ = 0.44769126161 rad
Angle ∠ B = β = 68.56987454962° = 68°34'7″ = 1.19767503729 rad
Angle ∠ C = γ = 85.82550477874° = 85°49'30″ = 1.49879296646 rad

Height: ha = 27.92656991776
Height: hb = 12.96655031896
Height: hc = 12.10111363103

Median: ma = 28.28798514848
Median: mb = 18.3988369493
Median: mc = 15.85987515272

Inradius: r = 5.11331561874
Circumradius: R = 15.0439909917

Vertex coordinates: A[30; 0] B[0; 0] C[4.75; 12.10111363103]
Centroid: CG[11.58333333333; 4.03437121034]
Coordinates of the circumscribed circle: U[15; 1.09549384967]
Coordinates of the inscribed circle: I[7.5; 5.11331561874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.3943793284° = 154°23'38″ = 0.44769126161 rad
∠ B' = β' = 111.4311254504° = 111°25'53″ = 1.19767503729 rad
∠ C' = γ' = 94.17549522126° = 94°10'30″ = 1.49879296646 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 = 13 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 13+28+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-13)(35.5-28)(35.5-30) } ; ; T = sqrt{ 32948.44 } = 181.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.52 }{ 13 } = 27.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.52 }{ 28 } = 12.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.52 }{ 30 } = 12.1 ; ;

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{ 13**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 25° 36'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 68° 34'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-28**2 }{ 2 * 28 * 13 } ) = 85° 49'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.52 }{ 35.5 } = 5.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 25° 36'22" } = 15.04 ; ;




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