7 9 13 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 9   c = 13

Area: T = 29.95330883216
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 30.79883817103° = 30°47'54″ = 0.53875331651 rad
Angle ∠ B = β = 41.17110828964° = 41°10'16″ = 0.71985709532 rad
Angle ∠ C = γ = 108.0310535393° = 108°1'50″ = 1.88554885353 rad

Height: ha = 8.55880252347
Height: hb = 6.65662418492
Height: hc = 4.60881674341

Median: ma = 10.61883802908
Median: mb = 9.42107218407
Median: mc = 4.77696960071

Inradius: r = 2.06657302291
Circumradius: R = 6.83656891217

Vertex coordinates: A[13; 0] B[0; 0] C[5.26992307692; 4.60881674341]
Centroid: CG[6.09897435897; 1.53660558114]
Coordinates of the circumscribed circle: U[6.5; -2.11658085377]
Coordinates of the inscribed circle: I[5.5; 2.06657302291]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.202161829° = 149°12'6″ = 0.53875331651 rad
∠ B' = β' = 138.8298917104° = 138°49'44″ = 0.71985709532 rad
∠ C' = γ' = 71.96994646067° = 71°58'10″ = 1.88554885353 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 = 9 ; ; c = 13 ; ;

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

p = a+b+c = 7+9+13 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-7)(14.5-9)(14.5-13) } ; ; T = sqrt{ 897.19 } = 29.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.95 }{ 7 } = 8.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.95 }{ 9 } = 6.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.95 }{ 13 } = 4.61 ; ;

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**2-9**2-13**2 }{ 2 * 9 * 13 } ) = 30° 47'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-7**2-13**2 }{ 2 * 7 * 13 } ) = 41° 10'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-7**2-9**2 }{ 2 * 9 * 7 } ) = 108° 1'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.95 }{ 14.5 } = 2.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 30° 47'54" } = 6.84 ; ;




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