15 29 30 triangle

Acute scalene triangle.

Sides: a = 15   b = 29   c = 30

Area: T = 213.5044098321
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 29.39440987412° = 29°23'39″ = 0.51330238037 rad
Angle ∠ B = β = 71.60656445746° = 71°36'20″ = 1.25497542608 rad
Angle ∠ C = γ = 799.0002566841° = 79°1″ = 1.37988145891 rad

Height: ha = 28.46772131095
Height: hb = 14.72444205739
Height: hc = 14.23436065548

Median: ma = 28.53550661468
Median: mb = 18.76883243791
Median: mc = 17.55499287748

Inradius: r = 5.77703810357
Circumradius: R = 15.28107371177

Vertex coordinates: A[30; 0] B[0; 0] C[4.73333333333; 14.23436065548]
Centroid: CG[11.57877777778; 4.74545355183]
Coordinates of the circumscribed circle: U[15; 2.91656348983]
Coordinates of the inscribed circle: I[8; 5.77703810357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6065901259° = 150°36'21″ = 0.51330238037 rad
∠ B' = β' = 108.3944355425° = 108°23'40″ = 1.25497542608 rad
∠ C' = γ' = 1010.999743316° = 100°59'59″ = 1.37988145891 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 = 15 ; ; b = 29 ; ; c = 30 ; ;

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

p = a+b+c = 15+29+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-15)(37-29)(37-30) } ; ; T = sqrt{ 45584 } = 213.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 213.5 }{ 15 } = 28.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 213.5 }{ 29 } = 14.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 213.5 }{ 30 } = 14.23 ; ;

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{ 15**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 29° 23'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 71° 36'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-29**2 }{ 2 * 29 * 15 } ) = 79° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 213.5 }{ 37 } = 5.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 29° 23'39" } = 15.28 ; ;




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