10 14 17 triangle

Acute scalene triangle.

Sides: a = 10   b = 14   c = 17

Area: T = 69.9788121581
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 36.01988541926° = 36°1'8″ = 0.62986475985 rad
Angle ∠ B = β = 55.41436895449° = 55°24'49″ = 0.96771513332 rad
Angle ∠ C = γ = 88.56774562624° = 88°34'3″ = 1.54657937219 rad

Height: ha = 13.99656243162
Height: hb = 9.99768745116
Height: hc = 8.2332720186

Median: ma = 14.74878812038
Median: mb = 12.06223380818
Median: mc = 8.70334475928

Inradius: r = 3.41435669064
Circumradius: R = 8.50326574958

Vertex coordinates: A[17; 0] B[0; 0] C[5.67664705882; 8.2332720186]
Centroid: CG[7.55988235294; 2.7444240062]
Coordinates of the circumscribed circle: U[8.5; 0.21325664374]
Coordinates of the inscribed circle: I[6.5; 3.41435669064]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.9811145807° = 143°58'52″ = 0.62986475985 rad
∠ B' = β' = 124.5866310455° = 124°35'11″ = 0.96771513332 rad
∠ C' = γ' = 91.43325437376° = 91°25'57″ = 1.54657937219 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 = 14 ; ; c = 17 ; ;

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

p = a+b+c = 10+14+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-10)(20.5-14)(20.5-17) } ; ; T = sqrt{ 4896.94 } = 69.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.98 }{ 10 } = 14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.98 }{ 14 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.98 }{ 17 } = 8.23 ; ;

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{ 10**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 36° 1'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 55° 24'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 88° 34'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.98 }{ 20.5 } = 3.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 36° 1'8" } = 8.5 ; ;




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