8 17 22 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 17   c = 22

Area: T = 59.59439384501
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 18.58333672856° = 18°35' = 0.32443409452 rad
Angle ∠ B = β = 42.62655262252° = 42°37'32″ = 0.7443955778 rad
Angle ∠ C = γ = 118.7911106489° = 118°47'28″ = 2.07332959303 rad

Height: ha = 14.89884846125
Height: hb = 7.01110515824
Height: hc = 5.41876307682

Median: ma = 19.24883765549
Median: mb = 14.20438727113
Median: mc = 7.45498322129

Inradius: r = 2.53659122745
Circumradius: R = 12.55216121178

Vertex coordinates: A[22; 0] B[0; 0] C[5.88663636364; 5.41876307682]
Centroid: CG[9.29554545455; 1.80658769227]
Coordinates of the circumscribed circle: U[11; -6.0455077895]
Coordinates of the inscribed circle: I[6.5; 2.53659122745]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4176632714° = 161°25' = 0.32443409452 rad
∠ B' = β' = 137.3744473775° = 137°22'28″ = 0.7443955778 rad
∠ C' = γ' = 61.20988935109° = 61°12'32″ = 2.07332959303 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 = 17 ; ; c = 22 ; ;

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

p = a+b+c = 8+17+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-8)(23.5-17)(23.5-22) } ; ; T = sqrt{ 3551.44 } = 59.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.59 }{ 8 } = 14.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.59 }{ 17 } = 7.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.59 }{ 22 } = 5.42 ; ;

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**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 18° 35' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-22**2 }{ 2 * 8 * 22 } ) = 42° 37'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 118° 47'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.59 }{ 23.5 } = 2.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 35' } = 12.55 ; ;




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