9 23 28 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 23   c = 28

Area: T = 93.9154855055
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 114.8532888602° = 114°51'10″ = 2.00545610615 rad

Height: ha = 20.876996779
Height: hb = 8.16765091352
Height: hc = 6.70882039325

Median: ma = 25.22439965113
Median: mb = 17.32877234512
Median: mc = 10.44403065089

Inradius: r = 3.13304951685
Circumradius: R = 15.42988690447

Vertex coordinates: A[28; 0] B[0; 0] C[6; 6.70882039325]
Centroid: CG[11.33333333333; 2.23660679775]
Coordinates of the circumscribed circle: U[14; -6.48545971347]
Coordinates of the inscribed circle: I[7; 3.13304951685]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 65.14771113984° = 65°8'50″ = 2.00545610615 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 = 9 ; ; b = 23 ; ; c = 28 ; ;

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

p = a+b+c = 9+23+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-9)(30-23)(30-28) } ; ; T = sqrt{ 8820 } = 93.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.91 }{ 9 } = 20.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.91 }{ 23 } = 8.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.91 }{ 28 } = 6.71 ; ;

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{ 9**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 16° 57'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-9**2-28**2 }{ 2 * 9 * 28 } ) = 48° 11'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-9**2-23**2 }{ 2 * 23 * 9 } ) = 114° 51'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.91 }{ 30 } = 3.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 16° 57'27" } = 15.43 ; ;




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