10 20 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 20   c = 26

Area: T = 89.87997772826
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 20.20552235834° = 20°12'19″ = 0.35326476776 rad
Angle ∠ B = β = 43.69108952793° = 43°41'27″ = 0.76325499758 rad
Angle ∠ C = γ = 116.1043881137° = 116°6'14″ = 2.02663950002 rad

Height: ha = 17.96599554565
Height: hb = 8.98799777283
Height: hc = 6.90876751756

Median: ma = 22.65495033058
Median: mb = 16.97105627485
Median: mc = 9

Inradius: r = 3.20771349029
Circumradius: R = 14.47766506036

Vertex coordinates: A[26; 0] B[0; 0] C[7.23107692308; 6.90876751756]
Centroid: CG[11.07769230769; 2.30325583919]
Coordinates of the circumscribed circle: U[13; -6.37697262656]
Coordinates of the inscribed circle: I[8; 3.20771349029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7954776417° = 159°47'41″ = 0.35326476776 rad
∠ B' = β' = 136.3099104721° = 136°18'33″ = 0.76325499758 rad
∠ C' = γ' = 63.89661188627° = 63°53'46″ = 2.02663950002 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 10+20+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-10)(28-20)(28-26) } ; ; T = sqrt{ 8064 } = 89.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.8 }{ 10 } = 17.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.8 }{ 20 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.8 }{ 26 } = 6.91 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 20° 12'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 43° 41'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-20**2 }{ 2 * 20 * 10 } ) = 116° 6'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.8 }{ 28 } = 3.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 20° 12'19" } = 14.48 ; ;




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