6 28 30 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 28   c = 30

Area: T = 81.58443122175
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 11.20108183696° = 11°12'3″ = 0.19554911595 rad
Angle ∠ B = β = 65.02550346323° = 65°1'30″ = 1.13549009506 rad
Angle ∠ C = γ = 103.7744146998° = 103°46'27″ = 1.81112005436 rad

Height: ha = 27.19547707392
Height: hb = 5.82774508727
Height: hc = 5.43989541478

Median: ma = 28.86217393793
Median: mb = 16.49224225025
Median: mc = 13.60114705087

Inradius: r = 2.55495097568
Circumradius: R = 15.44441456421

Vertex coordinates: A[30; 0] B[0; 0] C[2.53333333333; 5.43989541478]
Centroid: CG[10.84444444444; 1.81329847159]
Coordinates of the circumscribed circle: U[15; -3.67771775338]
Coordinates of the inscribed circle: I[4; 2.55495097568]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.799918163° = 168°47'57″ = 0.19554911595 rad
∠ B' = β' = 114.9754965368° = 114°58'30″ = 1.13549009506 rad
∠ C' = γ' = 76.2265853002° = 76°13'33″ = 1.81112005436 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 = 28 ; ; c = 30 ; ;

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

p = a+b+c = 6+28+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-6)(32-28)(32-30) } ; ; T = sqrt{ 6656 } = 81.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.58 }{ 6 } = 27.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.58 }{ 28 } = 5.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.58 }{ 30 } = 5.44 ; ;

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{ 6**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 11° 12'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-6**2-30**2 }{ 2 * 6 * 30 } ) = 65° 1'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-6**2-28**2 }{ 2 * 28 * 6 } ) = 103° 46'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.58 }{ 32 } = 2.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 12'3" } = 15.44 ; ;




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