11 22 30 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 30

Area: T = 95.92767298515
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 16.89990937835° = 16°53'57″ = 0.29549448271 rad
Angle ∠ B = β = 35.54772490891° = 35°32'50″ = 0.62204165366 rad
Angle ∠ C = γ = 127.5543657127° = 127°33'13″ = 2.22662312898 rad

Height: ha = 17.44112236094
Height: hb = 8.72106118047
Height: hc = 6.39551153234

Median: ma = 25.72545019388
Median: mb = 19.7365754356
Median: mc = 8.80334084308

Inradius: r = 3.04552930112
Circumradius: R = 18.92106908524

Vertex coordinates: A[30; 0] B[0; 0] C[8.95; 6.39551153234]
Centroid: CG[12.98333333333; 2.13217051078]
Coordinates of the circumscribed circle: U[15; -11.53222392592]
Coordinates of the inscribed circle: I[9.5; 3.04552930112]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.1010906217° = 163°6'3″ = 0.29549448271 rad
∠ B' = β' = 144.4532750911° = 144°27'10″ = 0.62204165366 rad
∠ C' = γ' = 52.44663428725° = 52°26'47″ = 2.22662312898 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 = 11 ; ; b = 22 ; ; c = 30 ; ;

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

p = a+b+c = 11+22+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-11)(31.5-22)(31.5-30) } ; ; T = sqrt{ 9201.94 } = 95.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.93 }{ 11 } = 17.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.93 }{ 22 } = 8.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.93 }{ 30 } = 6.4 ; ;

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{ 11**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 16° 53'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 35° 32'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 127° 33'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.93 }{ 31.5 } = 3.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 16° 53'57" } = 18.92 ; ;




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