8 15 22 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 15   c = 22

Area: T = 34.97876714491
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 12.23987557679° = 12°14'20″ = 0.21436065845 rad
Angle ∠ B = β = 23.42203319282° = 23°25'13″ = 0.40987619041 rad
Angle ∠ C = γ = 144.3410912304° = 144°20'27″ = 2.5199224165 rad

Height: ha = 8.74444178623
Height: hb = 4.66436895265
Height: hc = 3.18797883136

Median: ma = 18.3988369493
Median: mb = 14.75663545634
Median: mc = 4.84876798574

Inradius: r = 1.55545631755
Circumradius: R = 18.86991806131

Vertex coordinates: A[22; 0] B[0; 0] C[7.34109090909; 3.18797883136]
Centroid: CG[9.78803030303; 1.06599294379]
Coordinates of the circumscribed circle: U[11; -15.33112092482]
Coordinates of the inscribed circle: I[7.5; 1.55545631755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.7611244232° = 167°45'40″ = 0.21436065845 rad
∠ B' = β' = 156.5879668072° = 156°34'47″ = 0.40987619041 rad
∠ C' = γ' = 35.65990876961° = 35°39'33″ = 2.5199224165 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 = 8 ; ; b = 15 ; ; c = 22 ; ;

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

p = a+b+c = 8+15+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-8)(22.5-15)(22.5-22) } ; ; T = sqrt{ 1223.44 } = 34.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.98 }{ 8 } = 8.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.98 }{ 15 } = 4.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.98 }{ 22 } = 3.18 ; ;

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{ 8**2-15**2-22**2 }{ 2 * 15 * 22 } ) = 12° 14'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-8**2-22**2 }{ 2 * 8 * 22 } ) = 23° 25'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-8**2-15**2 }{ 2 * 15 * 8 } ) = 144° 20'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.98 }{ 22.5 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 12° 14'20" } = 18.87 ; ;




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