9 11 17 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 11   c = 17

Area: T = 44.46655765733
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 28.39663170018° = 28°23'47″ = 0.49656092271 rad
Angle ∠ B = β = 35.53884645156° = 35°32'18″ = 0.62202632169 rad
Angle ∠ C = γ = 116.0655218483° = 116°3'55″ = 2.02657202096 rad

Height: ha = 9.88112392385
Height: hb = 8.08546502861
Height: hc = 5.23112443027

Median: ma = 13.59222772191
Median: mb = 12.44398553046
Median: mc = 5.36219026474

Inradius: r = 2.40435446796
Circumradius: R = 9.46223758967

Vertex coordinates: A[17; 0] B[0; 0] C[7.32435294118; 5.23112443027]
Centroid: CG[8.10878431373; 1.74437481009]
Coordinates of the circumscribed circle: U[8.5; -4.15877106213]
Coordinates of the inscribed circle: I[7.5; 2.40435446796]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.6043682998° = 151°36'13″ = 0.49656092271 rad
∠ B' = β' = 144.4621535484° = 144°27'42″ = 0.62202632169 rad
∠ C' = γ' = 63.93547815174° = 63°56'5″ = 2.02657202096 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 = 11 ; ; c = 17 ; ;

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

p = a+b+c = 9+11+17 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-9)(18.5-11)(18.5-17) } ; ; T = sqrt{ 1977.19 } = 44.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.47 }{ 9 } = 9.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.47 }{ 11 } = 8.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.47 }{ 17 } = 5.23 ; ;

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**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 28° 23'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-9**2-17**2 }{ 2 * 9 * 17 } ) = 35° 32'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-9**2-11**2 }{ 2 * 11 * 9 } ) = 116° 3'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.47 }{ 18.5 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 28° 23'47" } = 9.46 ; ;




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