7 24 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 24   c = 26

Area: T = 83.02767276243
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 15.43329972651° = 15°25'59″ = 0.26993566157 rad
Angle ∠ B = β = 65.8376577219° = 65°50'12″ = 1.14990650407 rad
Angle ∠ C = γ = 98.73304255159° = 98°43'50″ = 1.72331709971 rad

Height: ha = 23.72219221784
Height: hb = 6.91988939687
Height: hc = 6.38766713557

Median: ma = 24.77439782837
Median: mb = 14.78217454991
Median: mc = 11.97991485507

Inradius: r = 2.91332185131
Circumradius: R = 13.15223911787

Vertex coordinates: A[26; 0] B[0; 0] C[2.86553846154; 6.38766713557]
Centroid: CG[9.62217948718; 2.12988904519]
Coordinates of the circumscribed circle: U[13; -1.99663450896]
Coordinates of the inscribed circle: I[4.5; 2.91332185131]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5677002735° = 164°34'1″ = 0.26993566157 rad
∠ B' = β' = 114.1633422781° = 114°9'48″ = 1.14990650407 rad
∠ C' = γ' = 81.27695744841° = 81°16'10″ = 1.72331709971 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 = 7 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 7+24+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-7)(28.5-24)(28.5-26) } ; ; T = sqrt{ 6893.44 } = 83.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.03 }{ 7 } = 23.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.03 }{ 24 } = 6.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.03 }{ 26 } = 6.39 ; ;

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{ 7**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 15° 25'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 65° 50'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 98° 43'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.03 }{ 28.5 } = 2.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 25'59" } = 13.15 ; ;




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