9 26 28 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 26   c = 28

Area: T = 116.8055126172
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 18.71769506574° = 18°43'1″ = 0.32766724149 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 93.30773621797° = 93°18'26″ = 1.62985206864 rad

Height: ha = 25.95766947048
Height: hb = 8.98550097055
Height: hc = 8.3433223298

Median: ma = 26.64111336095
Median: mb = 16.23326830807
Median: mc = 13.50992560861

Inradius: r = 3.70880992435
Circumradius: R = 14.02333571392

Vertex coordinates: A[28; 0] B[0; 0] C[3.375; 8.3433223298]
Centroid: CG[10.45883333333; 2.78110744327]
Coordinates of the circumscribed circle: U[14; -0.8099039835]
Coordinates of the inscribed circle: I[5.5; 3.70880992435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.2833049343° = 161°16'59″ = 0.32766724149 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 86.69326378203° = 86°41'34″ = 1.62985206864 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 = 9 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 9+26+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-9)(31.5-26)(31.5-28) } ; ; T = sqrt{ 13643.44 } = 116.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 116.81 }{ 9 } = 25.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 116.81 }{ 26 } = 8.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 116.81 }{ 28 } = 8.34 ; ;

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{ 9**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 18° 43'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-9**2-28**2 }{ 2 * 9 * 28 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-9**2-26**2 }{ 2 * 26 * 9 } ) = 93° 18'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 116.81 }{ 31.5 } = 3.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 43'1" } = 14.02 ; ;




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