6 21 26 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 21   c = 26

Area: T = 38.65114876816
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 8.13993156701° = 8°8'22″ = 0.14220578573 rad
Angle ∠ B = β = 29.70548301032° = 29°42'17″ = 0.5188447089 rad
Angle ∠ C = γ = 142.1565854227° = 142°9'21″ = 2.48110877072 rad

Height: ha = 12.88438292272
Height: hb = 3.68110940649
Height: hc = 2.97331913601

Median: ma = 23.44114163395
Median: mb = 15.67664154066
Median: mc = 8.33766660003

Inradius: r = 1.4598546705
Circumradius: R = 21.18993525741

Vertex coordinates: A[26; 0] B[0; 0] C[5.21215384615; 2.97331913601]
Centroid: CG[10.40438461538; 0.99110637867]
Coordinates of the circumscribed circle: U[13; -16.7332861755]
Coordinates of the inscribed circle: I[5.5; 1.4598546705]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.861068433° = 171°51'38″ = 0.14220578573 rad
∠ B' = β' = 150.2955169897° = 150°17'43″ = 0.5188447089 rad
∠ C' = γ' = 37.84441457733° = 37°50'39″ = 2.48110877072 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 = 6 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 6+21+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 * (26.5-6)(26.5-21)(26.5-26) } ; ; T = sqrt{ 1493.94 } = 38.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.65 }{ 6 } = 12.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.65 }{ 21 } = 3.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.65 }{ 26 } = 2.97 ; ;

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{ 6**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 8° 8'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-6**2-26**2 }{ 2 * 6 * 26 } ) = 29° 42'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-6**2-21**2 }{ 2 * 21 * 6 } ) = 142° 9'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.65 }{ 26.5 } = 1.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 8° 8'22" } = 21.19 ; ;




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