9 18 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 18   c = 22

Area: T = 78.55553149061
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 23.37547882659° = 23°22'29″ = 0.40879670172 rad
Angle ∠ B = β = 52.51326785757° = 52°30'46″ = 0.91765191402 rad
Angle ∠ C = γ = 104.1132533158° = 104°6'45″ = 1.81771064962 rad

Height: ha = 17.45767366458
Height: hb = 8.72883683229
Height: hc = 7.14113922642

Median: ma = 19.59895380242
Median: mb = 14.19550695666
Median: mc = 9.02877350426

Inradius: r = 3.20663393839
Circumradius: R = 11.34223261184

Vertex coordinates: A[22; 0] B[0; 0] C[5.47772727273; 7.14113922642]
Centroid: CG[9.15990909091; 2.38804640881]
Coordinates of the circumscribed circle: U[11; -2.76655671708]
Coordinates of the inscribed circle: I[6.5; 3.20663393839]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.6255211734° = 156°37'31″ = 0.40879670172 rad
∠ B' = β' = 127.4877321424° = 127°29'14″ = 0.91765191402 rad
∠ C' = γ' = 75.88774668416° = 75°53'15″ = 1.81771064962 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 = 9 ; ; b = 18 ; ; c = 22 ; ;

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

p = a+b+c = 9+18+22 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-9)(24.5-18)(24.5-22) } ; ; T = sqrt{ 6170.94 } = 78.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.56 }{ 9 } = 17.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.56 }{ 18 } = 8.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.56 }{ 22 } = 7.14 ; ;

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{ 9**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 23° 22'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 52° 30'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-18**2 }{ 2 * 18 * 9 } ) = 104° 6'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.56 }{ 24.5 } = 3.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 23° 22'29" } = 11.34 ; ;




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