15 26 29 triangle

Acute scalene triangle.

Sides: a = 15   b = 26   c = 29

Area: T = 194.4222220952
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 31.04548445349° = 31°2'41″ = 0.54218347529 rad
Angle ∠ B = β = 63.36768812508° = 63°22'1″ = 1.10659607145 rad
Angle ∠ C = γ = 85.58882742142° = 85°35'18″ = 1.49437971861 rad

Height: ha = 25.92329627936
Height: hb = 14.95655554579
Height: hc = 13.40884290312

Median: ma = 26.5
Median: mb = 19.07987840283
Median: mc = 15.5

Inradius: r = 5.55549205986
Circumradius: R = 14.54330907339

Vertex coordinates: A[29; 0] B[0; 0] C[6.7244137931; 13.40884290312]
Centroid: CG[11.9088045977; 4.46994763437]
Coordinates of the circumscribed circle: U[14.5; 1.11986992872]
Coordinates of the inscribed circle: I[9; 5.55549205986]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.9555155465° = 148°57'19″ = 0.54218347529 rad
∠ B' = β' = 116.6333118749° = 116°37'59″ = 1.10659607145 rad
∠ C' = γ' = 94.41217257858° = 94°24'42″ = 1.49437971861 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 = 15 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 15+26+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-15)(35-26)(35-29) } ; ; T = sqrt{ 37800 } = 194.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.42 }{ 15 } = 25.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.42 }{ 26 } = 14.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.42 }{ 29 } = 13.41 ; ;

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{ 15**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 31° 2'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 63° 22'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-26**2 }{ 2 * 26 * 15 } ) = 85° 35'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.42 }{ 35 } = 5.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 2'41" } = 14.54 ; ;




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