9 10 17 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 17

Area: T = 36
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 25.05876154183° = 25°3'27″ = 0.43773378917 rad
Angle ∠ B = β = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ C = γ = 126.8769897646° = 126°52'12″ = 2.21442974356 rad

Height: ha = 8
Height: hb = 7.2
Height: hc = 4.23552941176

Median: ma = 13.22003787824
Median: mb = 12.64991106407
Median: mc = 4.27220018727

Inradius: r = 2
Circumradius: R = 10.625

Vertex coordinates: A[17; 0] B[0; 0] C[7.94111764706; 4.23552941176]
Centroid: CG[8.31437254902; 1.41217647059]
Coordinates of the circumscribed circle: U[8.5; -6.375]
Coordinates of the inscribed circle: I[8; 2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9422384582° = 154°56'33″ = 0.43773378917 rad
∠ B' = β' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ C' = γ' = 53.13301023542° = 53°7'48″ = 2.21442974356 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 = 10 ; ; c = 17 ; ;

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

p = a+b+c = 9+10+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-9)(18-10)(18-17) } ; ; T = sqrt{ 1296 } = 36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36 }{ 9 } = 8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36 }{ 10 } = 7.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36 }{ 17 } = 4.24 ; ;

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**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 25° 3'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-9**2-17**2 }{ 2 * 9 * 17 } ) = 28° 4'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-9**2-10**2 }{ 2 * 10 * 9 } ) = 126° 52'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36 }{ 18 } = 2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 25° 3'27" } = 10.63 ; ;




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