5 15 17 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 15   c = 17

Area: T = 36.21103231137
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 16.49992344912° = 16°29'57″ = 0.28879659659 rad
Angle ∠ B = β = 58.43107033639° = 58°25'51″ = 1.0219808158 rad
Angle ∠ C = γ = 105.0770062145° = 105°4'12″ = 1.83438185297 rad

Height: ha = 14.48441292455
Height: hb = 4.82880430818
Height: hc = 4.26600380134

Median: ma = 15.83550876221
Median: mb = 10.03774299499
Median: mc = 7.26329195232

Inradius: r = 1.95773147629
Circumradius: R = 8.80327383517

Vertex coordinates: A[17; 0] B[0; 0] C[2.61876470588; 4.26600380134]
Centroid: CG[6.53992156863; 1.42200126711]
Coordinates of the circumscribed circle: U[8.5; -2.28987119714]
Coordinates of the inscribed circle: I[3.5; 1.95773147629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.5010765509° = 163°30'3″ = 0.28879659659 rad
∠ B' = β' = 121.5699296636° = 121°34'9″ = 1.0219808158 rad
∠ C' = γ' = 74.93299378551° = 74°55'48″ = 1.83438185297 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 = 5 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 5+15+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 * (18.5-5)(18.5-15)(18.5-17) } ; ; T = sqrt{ 1311.19 } = 36.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.21 }{ 5 } = 14.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.21 }{ 15 } = 4.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.21 }{ 17 } = 4.26 ; ;

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{ 5**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 16° 29'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-5**2-17**2 }{ 2 * 5 * 17 } ) = 58° 25'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-5**2-15**2 }{ 2 * 15 * 5 } ) = 105° 4'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.21 }{ 18.5 } = 1.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 16° 29'57" } = 8.8 ; ;




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