15 22 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 22   c = 29

Area: T = 161.6666323024
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 30.45503140214° = 30°27'1″ = 0.53114582379 rad
Angle ∠ B = β = 48.01327269458° = 48°46″ = 0.83879801681 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 21.55655097365
Height: hb = 14.69769384567
Height: hc = 11.14994015878

Median: ma = 24.62221445045
Median: mb = 20.29877831302
Median: mc = 12.01104121495

Inradius: r = 4.89989794856
Circumradius: R = 14.79990005293

Vertex coordinates: A[29; 0] B[0; 0] C[10.03444827586; 11.14994015878]
Centroid: CG[13.01114942529; 3.71664671959]
Coordinates of the circumscribed circle: U[14.5; -2.96598001059]
Coordinates of the inscribed circle: I[11; 4.89989794856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.5549685979° = 149°32'59″ = 0.53114582379 rad
∠ B' = β' = 131.9877273054° = 131°59'14″ = 0.83879801681 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 15+22+29 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-15)(33-22)(33-29) } ; ; T = sqrt{ 26136 } = 161.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.67 }{ 15 } = 21.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.67 }{ 22 } = 14.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.67 }{ 29 } = 11.15 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 30° 27'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 48° 46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-22**2 }{ 2 * 22 * 15 } ) = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.67 }{ 33 } = 4.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° 27'1" } = 14.8 ; ;




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