10 11 17 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 11   c = 17

Area: T = 52.30767873225
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 34.01664484671° = 34°59″ = 0.59436990256 rad
Angle ∠ B = β = 37.97990985328° = 37°58'45″ = 0.66328603163 rad
Angle ∠ C = γ = 108.0044453° = 108°16″ = 1.88550333117 rad

Height: ha = 10.46113574645
Height: hb = 9.51103249677
Height: hc = 6.1543739685

Median: ma = 13.4166407865
Median: mb = 12.8166005618
Median: mc = 6.18546584384

Inradius: r = 2.75329888064
Circumradius: R = 8.9387654632

Vertex coordinates: A[17; 0] B[0; 0] C[7.88223529412; 6.1543739685]
Centroid: CG[8.29441176471; 2.05112465617]
Coordinates of the circumscribed circle: U[8.5; -2.76325477954]
Coordinates of the inscribed circle: I[8; 2.75329888064]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.9843551533° = 145°59'1″ = 0.59436990256 rad
∠ B' = β' = 142.0210901467° = 142°1'15″ = 0.66328603163 rad
∠ C' = γ' = 71.99655469999° = 71°59'44″ = 1.88550333117 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 = 10 ; ; b = 11 ; ; c = 17 ; ;

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

p = a+b+c = 10+11+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-10)(19-11)(19-17) } ; ; T = sqrt{ 2736 } = 52.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.31 }{ 10 } = 10.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.31 }{ 11 } = 9.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.31 }{ 17 } = 6.15 ; ;

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{ 10**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 34° 59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 37° 58'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 108° 16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.31 }{ 19 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 34° 59" } = 8.94 ; ;




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