7 28 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 28   c = 30

Area: T = 96.55879489219
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 13.2911177243° = 13°17'28″ = 0.23219748044 rad
Angle ∠ B = β = 66.86876036007° = 66°52'3″ = 1.16770598458 rad
Angle ∠ C = γ = 99.84112191563° = 99°50'28″ = 1.74325580035 rad

Height: ha = 27.58879854063
Height: hb = 6.89769963516
Height: hc = 6.43771965948

Median: ma = 28.80553814417
Median: mb = 16.68883192683
Median: mc = 13.83883525031

Inradius: r = 2.9711013813
Circumradius: R = 15.22440184927

Vertex coordinates: A[30; 0] B[0; 0] C[2.75; 6.43771965948]
Centroid: CG[10.91766666667; 2.14657321983]
Coordinates of the circumscribed circle: U[15; -2.60220643852]
Coordinates of the inscribed circle: I[4.5; 2.9711013813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.7098822757° = 166°42'32″ = 0.23219748044 rad
∠ B' = β' = 113.1322396399° = 113°7'57″ = 1.16770598458 rad
∠ C' = γ' = 80.15987808437° = 80°9'32″ = 1.74325580035 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 = 7 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 7+28+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-7)(32.5-28)(32.5-30) } ; ; T = sqrt{ 9323.44 } = 96.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 96.56 }{ 7 } = 27.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96.56 }{ 28 } = 6.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96.56 }{ 30 } = 6.44 ; ;

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{ 7**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 13° 17'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 66° 52'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-28**2 }{ 2 * 28 * 7 } ) = 99° 50'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96.56 }{ 32.5 } = 2.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 17'28" } = 15.22 ; ;




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