15 24 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 24   c = 29

Area: T = 179.7222007556
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 31.09439258976° = 31°5'38″ = 0.54326913843 rad
Angle ∠ B = β = 55.72113355656° = 55°43'17″ = 0.97325207692 rad
Angle ∠ C = γ = 93.18547385367° = 93°11'5″ = 1.62663805001 rad

Height: ha = 23.96329343408
Height: hb = 14.9776833963
Height: hc = 12.39546212108

Median: ma = 25.53991855782
Median: mb = 19.72330829233
Median: mc = 13.79331142241

Inradius: r = 5.28659413987
Circumradius: R = 14.52224284743

Vertex coordinates: A[29; 0] B[0; 0] C[8.44882758621; 12.39546212108]
Centroid: CG[12.48327586207; 4.13215404036]
Coordinates of the circumscribed circle: U[14.5; -0.80768015819]
Coordinates of the inscribed circle: I[10; 5.28659413987]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.9066074102° = 148°54'22″ = 0.54326913843 rad
∠ B' = β' = 124.2798664434° = 124°16'43″ = 0.97325207692 rad
∠ C' = γ' = 86.81552614633° = 86°48'55″ = 1.62663805001 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 = 24 ; ; c = 29 ; ;

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

p = a+b+c = 15+24+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-15)(34-24)(34-29) } ; ; T = sqrt{ 32300 } = 179.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 179.72 }{ 15 } = 23.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 179.72 }{ 24 } = 14.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 179.72 }{ 29 } = 12.39 ; ;

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**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 31° 5'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 55° 43'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-24**2 }{ 2 * 24 * 15 } ) = 93° 11'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 179.72 }{ 34 } = 5.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 5'38" } = 14.52 ; ;




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