17 26 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 26   c = 28

Area: T = 216.3187908413
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 36.46113196683° = 36°27'41″ = 0.63663700778 rad
Angle ∠ B = β = 65.35436112305° = 65°21'13″ = 1.1410635694 rad
Angle ∠ C = γ = 78.18550691012° = 78°11'6″ = 1.36545868817 rad

Height: ha = 25.44991656956
Height: hb = 16.64398391087
Height: hc = 15.45112791723

Median: ma = 25.64766372065
Median: mb = 19.17702895127
Median: mc = 16.92663108798

Inradius: r = 6.09334622088
Circumradius: R = 14.30330229106

Vertex coordinates: A[28; 0] B[0; 0] C[7.08992857143; 15.45112791723]
Centroid: CG[11.69664285714; 5.15504263908]
Coordinates of the circumscribed circle: U[14; 2.92985601208]
Coordinates of the inscribed circle: I[9.5; 6.09334622088]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5398680332° = 143°32'19″ = 0.63663700778 rad
∠ B' = β' = 114.646638877° = 114°38'47″ = 1.1410635694 rad
∠ C' = γ' = 101.8154930899° = 101°48'54″ = 1.36545868817 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 = 17 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 17+26+28 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-17)(35.5-26)(35.5-28) } ; ; T = sqrt{ 46793.44 } = 216.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 216.32 }{ 17 } = 25.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 216.32 }{ 26 } = 16.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 216.32 }{ 28 } = 15.45 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 26**2+28**2-17**2 }{ 2 * 26 * 28 } ) = 36° 27'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+28**2-26**2 }{ 2 * 17 * 28 } ) = 65° 21'13" ; ; gamma = 180° - alpha - beta = 180° - 36° 27'41" - 65° 21'13" = 78° 11'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 216.32 }{ 35.5 } = 6.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 36° 27'41" } = 14.3 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 17**2 } }{ 2 } = 25.647 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 17**2 - 26**2 } }{ 2 } = 19.17 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 17**2 - 28**2 } }{ 2 } = 16.926 ; ;
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