13 22 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 30

Area: T = 128.9880376414
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 23.00773759133° = 23°27″ = 0.40215544619 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 115.5833001977° = 115°34'59″ = 2.01773039438 rad

Height: ha = 19.8433134833
Height: hb = 11.72554887649
Height: hc = 8.5998691761

Median: ma = 25.49901941931
Median: mb = 20.33546994077
Median: mc = 10.07547208398

Inradius: r = 3.96986269666
Circumradius: R = 16.63304368124

Vertex coordinates: A[30; 0] B[0; 0] C[9.75; 8.5998691761]
Centroid: CG[13.25; 2.8666230587]
Coordinates of the circumscribed circle: U[15; -7.18113249872]
Coordinates of the inscribed circle: I[10.5; 3.96986269666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9932624087° = 156°59'33″ = 0.40215544619 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 64.41769980226° = 64°25'1″ = 2.01773039438 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 = 13 ; ; b = 22 ; ; c = 30 ; ;

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

p = a+b+c = 13+22+30 = 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 * (32.5-13)(32.5-22)(32.5-30) } ; ; T = sqrt{ 16635.94 } = 128.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 128.98 }{ 13 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 128.98 }{ 22 } = 11.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 128.98 }{ 30 } = 8.6 ; ;

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{ 13**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 23° 27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 41° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-22**2 }{ 2 * 22 * 13 } ) = 115° 34'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 128.98 }{ 32.5 } = 3.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 23° 27" } = 16.63 ; ;




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