7 20 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 26

Area: T = 40.9810940692
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 9.0698721546° = 9°4'7″ = 0.15882790499 rad
Angle ∠ B = β = 26.76655005768° = 26°45'56″ = 0.4677146111 rad
Angle ∠ C = γ = 144.1665777877° = 144°9'57″ = 2.51661674927 rad

Height: ha = 11.70988401977
Height: hb = 4.09880940692
Height: hc = 3.15223800532

Median: ma = 22.92992389756
Median: mb = 16.2021851746
Median: mc = 7.45498322129

Inradius: r = 1.54664505922
Circumradius: R = 22.20554444001

Vertex coordinates: A[26; 0] B[0; 0] C[6.25; 3.15223800532]
Centroid: CG[10.75; 1.05107933511]
Coordinates of the circumscribed circle: U[13; -18.00222709958]
Coordinates of the inscribed circle: I[6.5; 1.54664505922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.9311278454° = 170°55'53″ = 0.15882790499 rad
∠ B' = β' = 153.2344499423° = 153°14'4″ = 0.4677146111 rad
∠ C' = γ' = 35.83442221228° = 35°50'3″ = 2.51661674927 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 7+20+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-7)(26.5-20)(26.5-26) } ; ; T = sqrt{ 1679.44 } = 40.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.98 }{ 7 } = 11.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.98 }{ 20 } = 4.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.98 }{ 26 } = 3.15 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 9° 4'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 26° 45'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 144° 9'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.98 }{ 26.5 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 9° 4'7" } = 22.21 ; ;




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