7 17 22 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 17   c = 22

Area: T = 46.98993604979
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 14.55332690751° = 14°33'12″ = 0.25440024623 rad
Angle ∠ B = β = 37.60876855758° = 37°36'28″ = 0.65663779374 rad
Angle ∠ C = γ = 127.8399045349° = 127°50'21″ = 2.23112122539 rad

Height: ha = 13.42655315708
Height: hb = 5.52881600586
Height: hc = 4.27217600453

Median: ma = 19.34655421222
Median: mb = 13.93773598648
Median: mc = 6.92882032303

Inradius: r = 2.04330156738
Circumradius: R = 13.92986849845

Vertex coordinates: A[22; 0] B[0; 0] C[5.54554545455; 4.27217600453]
Centroid: CG[9.18218181818; 1.42439200151]
Coordinates of the circumscribed circle: U[11; -8.54444874275]
Coordinates of the inscribed circle: I[6; 2.04330156738]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.4476730925° = 165°26'48″ = 0.25440024623 rad
∠ B' = β' = 142.3922314424° = 142°23'32″ = 0.65663779374 rad
∠ C' = γ' = 52.16109546509° = 52°9'39″ = 2.23112122539 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 = 7 ; ; b = 17 ; ; c = 22 ; ;

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

p = a+b+c = 7+17+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-7)(23-17)(23-22) } ; ; T = sqrt{ 2208 } = 46.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.99 }{ 7 } = 13.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.99 }{ 17 } = 5.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.99 }{ 22 } = 4.27 ; ;

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{ 7**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 14° 33'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-22**2 }{ 2 * 7 * 22 } ) = 37° 36'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 127° 50'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.99 }{ 23 } = 2.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 33'12" } = 13.93 ; ;




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