7 23 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 23   c = 29

Area: T = 46.44655326162
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 8.00554308657° = 8°20″ = 0.14397211266 rad
Angle ∠ B = β = 27.23217973292° = 27°13'54″ = 0.47552845246 rad
Angle ∠ C = γ = 144.7632771805° = 144°45'46″ = 2.52765870023 rad

Height: ha = 13.2770152176
Height: hb = 4.03987419666
Height: hc = 3.20331401804

Median: ma = 25.93774246987
Median: mb = 17.68547391838
Median: mc = 8.87441196746

Inradius: r = 1.57444248344
Circumradius: R = 25.13215882121

Vertex coordinates: A[29; 0] B[0; 0] C[6.2244137931; 3.20331401804]
Centroid: CG[11.74113793103; 1.06877133935]
Coordinates of the circumscribed circle: U[14.5; -20.52767319869]
Coordinates of the inscribed circle: I[6.5; 1.57444248344]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.9954569134° = 171°59'40″ = 0.14397211266 rad
∠ B' = β' = 152.7688202671° = 152°46'6″ = 0.47552845246 rad
∠ C' = γ' = 35.23772281949° = 35°14'14″ = 2.52765870023 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 = 23 ; ; c = 29 ; ;

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

p = a+b+c = 7+23+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-7)(29.5-23)(29.5-29) } ; ; T = sqrt{ 2157.19 } = 46.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.45 }{ 7 } = 13.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.45 }{ 23 } = 4.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.45 }{ 29 } = 3.2 ; ;

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**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 8° 20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 27° 13'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 144° 45'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.45 }{ 29.5 } = 1.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 8° 20" } = 25.13 ; ;




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