9 15 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 15   c = 22

Area: T = 50.75443101618
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 17.91547679103° = 17°54'53″ = 0.31326716848 rad
Angle ∠ B = β = 30.84218279549° = 30°50'31″ = 0.53882914451 rad
Angle ∠ C = γ = 131.2433404135° = 131°14'36″ = 2.29106295237 rad

Height: ha = 11.27987355915
Height: hb = 6.76772413549
Height: hc = 4.61440281965

Median: ma = 18.28325052988
Median: mb = 15.04216089565
Median: mc = 5.65768542495

Inradius: r = 2.20767091375
Circumradius: R = 14.62992994158

Vertex coordinates: A[22; 0] B[0; 0] C[7.72772727273; 4.61440281965]
Centroid: CG[9.90990909091; 1.53880093988]
Coordinates of the circumscribed circle: U[11; -9.64545010964]
Coordinates of the inscribed circle: I[8; 2.20767091375]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.085523209° = 162°5'7″ = 0.31326716848 rad
∠ B' = β' = 149.1588172045° = 149°9'29″ = 0.53882914451 rad
∠ C' = γ' = 48.75765958652° = 48°45'24″ = 2.29106295237 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 = 15 ; ; c = 22 ; ;

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

p = a+b+c = 9+15+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 * (23-9)(23-15)(23-22) } ; ; T = sqrt{ 2576 } = 50.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.75 }{ 9 } = 11.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.75 }{ 15 } = 6.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.75 }{ 22 } = 4.61 ; ;

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**2-15**2-22**2 }{ 2 * 15 * 22 } ) = 17° 54'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 30° 50'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-15**2 }{ 2 * 15 * 9 } ) = 131° 14'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.75 }{ 23 } = 2.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 54'53" } = 14.63 ; ;




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