15 23 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 23   c = 29

Area: T = 171.1233310802
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 30.87114335686° = 30°52'17″ = 0.53988081606 rad
Angle ∠ B = β = 51.88550359596° = 51°53'6″ = 0.906556471 rad
Angle ∠ C = γ = 97.24435304718° = 97°14'37″ = 1.6977219783 rad

Height: ha = 22.81664414403
Height: hb = 14.88802878959
Height: hc = 11.80216076415

Median: ma = 25.07548878362
Median: mb = 20.01987412192
Median: mc = 12.91331715701

Inradius: r = 5.10881585314
Circumradius: R = 14.61766526832

Vertex coordinates: A[29; 0] B[0; 0] C[9.25986206897; 11.80216076415]
Centroid: CG[12.75328735632; 3.93438692138]
Coordinates of the circumscribed circle: U[14.5; -1.84329692514]
Coordinates of the inscribed circle: I[10.5; 5.10881585314]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.1298566431° = 149°7'43″ = 0.53988081606 rad
∠ B' = β' = 128.115496404° = 128°6'54″ = 0.906556471 rad
∠ C' = γ' = 82.75664695282° = 82°45'23″ = 1.6977219783 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 = 23 ; ; c = 29 ; ;

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

p = a+b+c = 15+23+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-15)(33.5-23)(33.5-29) } ; ; T = sqrt{ 29283.19 } = 171.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.12 }{ 15 } = 22.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.12 }{ 23 } = 14.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.12 }{ 29 } = 11.8 ; ;

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**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 30° 52'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 51° 53'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-23**2 }{ 2 * 23 * 15 } ) = 97° 14'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.12 }{ 33.5 } = 5.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° 52'17" } = 14.62 ; ;




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