10 15 23 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 15   c = 23

Area: T = 54.99109083395
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 18.59896365026° = 18°35'23″ = 0.32444503637 rad
Angle ∠ B = β = 28.56767204538° = 28°34' = 0.49985833284 rad
Angle ∠ C = γ = 132.8443643044° = 132°50'37″ = 2.31985589615 rad

Height: ha = 10.99881816679
Height: hb = 7.33221211119
Height: hc = 4.78218181165

Median: ma = 18.76216630393
Median: mb = 16.077015868
Median: mc = 5.5

Inradius: r = 2.29112878475
Circumradius: R = 15.68444108607

Vertex coordinates: A[23; 0] B[0; 0] C[8.78326086957; 4.78218181165]
Centroid: CG[10.59442028986; 1.59439393722]
Coordinates of the circumscribed circle: U[11.5; -10.66553993853]
Coordinates of the inscribed circle: I[9; 2.29112878475]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4110363497° = 161°24'37″ = 0.32444503637 rad
∠ B' = β' = 151.4333279546° = 151°26' = 0.49985833284 rad
∠ C' = γ' = 47.15663569564° = 47°9'23″ = 2.31985589615 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 = 15 ; ; c = 23 ; ;

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

p = a+b+c = 10+15+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-10)(24-15)(24-23) } ; ; T = sqrt{ 3024 } = 54.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.99 }{ 10 } = 11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.99 }{ 15 } = 7.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.99 }{ 23 } = 4.78 ; ;

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**2-15**2-23**2 }{ 2 * 15 * 23 } ) = 18° 35'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-23**2 }{ 2 * 10 * 23 } ) = 28° 34' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 132° 50'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.99 }{ 24 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 35'23" } = 15.68 ; ;




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