15 21 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 21   c = 29

Area: T = 151.3021644076
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 29.79441613936° = 29°47'39″ = 0.52200062142 rad
Angle ∠ B = β = 44.07882183933° = 44°4'42″ = 0.76993100394 rad
Angle ∠ C = γ = 106.1287620213° = 106°7'39″ = 1.85222764 rad

Height: ha = 20.17435525434
Height: hb = 14.41096803882
Height: hc = 10.43545961431

Median: ma = 24.18216045787
Median: mb = 20.5610885195
Median: mc = 11.07992599031

Inradius: r = 4.65554352023
Circumradius: R = 15.09440197243

Vertex coordinates: A[29; 0] B[0; 0] C[10.7765862069; 10.43545961431]
Centroid: CG[13.25986206897; 3.47881987144]
Coordinates of the circumscribed circle: U[14.5; -4.19327832568]
Coordinates of the inscribed circle: I[11.5; 4.65554352023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2065838606° = 150°12'21″ = 0.52200062142 rad
∠ B' = β' = 135.9221781607° = 135°55'18″ = 0.76993100394 rad
∠ C' = γ' = 73.87223797868° = 73°52'21″ = 1.85222764 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 = 21 ; ; c = 29 ; ;

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

p = a+b+c = 15+21+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-15)(32.5-21)(32.5-29) } ; ; T = sqrt{ 22892.19 } = 151.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.3 }{ 15 } = 20.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.3 }{ 21 } = 14.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.3 }{ 29 } = 10.43 ; ;

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**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 29° 47'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 44° 4'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-21**2 }{ 2 * 21 * 15 } ) = 106° 7'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.3 }{ 32.5 } = 4.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 29° 47'39" } = 15.09 ; ;




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