10 17 23 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 17   c = 23

Area: T = 77.46596669241
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 23.34216553766° = 23°20'30″ = 0.40773887392 rad
Angle ∠ B = β = 42.34326054522° = 42°20'33″ = 0.7399017879 rad
Angle ∠ C = γ = 114.3165739171° = 114°18'57″ = 1.99551860354 rad

Height: ha = 15.49219333848
Height: hb = 9.11329019911
Height: hc = 6.73656232108

Median: ma = 19.59659179423
Median: mb = 15.56443824163
Median: mc = 7.8989866919

Inradius: r = 3.0988386677
Circumradius: R = 12.61994707364

Vertex coordinates: A[23; 0] B[0; 0] C[7.39113043478; 6.73656232108]
Centroid: CG[10.13304347826; 2.24552077369]
Coordinates of the circumscribed circle: U[11.5; -5.19662526562]
Coordinates of the inscribed circle: I[8; 3.0988386677]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.6588344623° = 156°39'30″ = 0.40773887392 rad
∠ B' = β' = 137.6577394548° = 137°39'27″ = 0.7399017879 rad
∠ C' = γ' = 65.68442608288° = 65°41'3″ = 1.99551860354 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 = 17 ; ; c = 23 ; ;

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

p = a+b+c = 10+17+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-10)(25-17)(25-23) } ; ; T = sqrt{ 6000 } = 77.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.46 }{ 10 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.46 }{ 17 } = 9.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.46 }{ 23 } = 6.74 ; ;

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**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 23° 20'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-23**2 }{ 2 * 10 * 23 } ) = 42° 20'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 114° 18'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.46 }{ 25 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 20'30" } = 12.62 ; ;




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