8 21 26 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 21   c = 26

Area: T = 72.30879352492
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ C = γ = 120.5922488745° = 120°35'33″ = 2.10547359818 rad

Height: ha = 18.07769838123
Height: hb = 6.88664700237
Height: hc = 5.56221488653

Median: ma = 23.29216293977
Median: mb = 16.11767614613
Median: mc = 9.13878334412

Inradius: r = 2.62993794636
Circumradius: R = 15.10220769192

Vertex coordinates: A[26; 0] B[0; 0] C[5.75; 5.56221488653]
Centroid: CG[10.58333333333; 1.85440496218]
Coordinates of the circumscribed circle: U[13; -7.68658784321]
Coordinates of the inscribed circle: I[6.5; 2.62993794636]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ C' = γ' = 59.40875112549° = 59°24'27″ = 2.10547359818 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 = 8 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 8+21+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-8)(27.5-21)(27.5-26) } ; ; T = sqrt{ 5228.44 } = 72.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.31 }{ 8 } = 18.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.31 }{ 21 } = 6.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.31 }{ 26 } = 5.56 ; ;

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{ 8**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 44° 2'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-21**2 }{ 2 * 21 * 8 } ) = 120° 35'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.31 }{ 27.5 } = 2.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 21'32" } = 15.1 ; ;




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