21 22 26 triangle

Acute scalene triangle.

Sides: a = 21   b = 22   c = 26

Area: T = 222.454434925
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 51.06107158057° = 51°3'39″ = 0.89111776092 rad
Angle ∠ B = β = 54.57326412751° = 54°34'22″ = 0.95224722718 rad
Angle ∠ C = γ = 74.36766429192° = 74°22' = 1.29879427726 rad

Height: ha = 21.18661284999
Height: hb = 20.2233122659
Height: hc = 17.11218730192

Median: ma = 21.67437168017
Median: mb = 20.91765006634
Median: mc = 17.1321841699

Inradius: r = 6.44879521522
Circumradius: R = 13.4999398911

Vertex coordinates: A[26; 0] B[0; 0] C[12.17330769231; 17.11218730192]
Centroid: CG[12.72443589744; 5.70439576731]
Coordinates of the circumscribed circle: U[13; 3.63878250312]
Coordinates of the inscribed circle: I[12.5; 6.44879521522]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9399284194° = 128°56'21″ = 0.89111776092 rad
∠ B' = β' = 125.4277358725° = 125°25'38″ = 0.95224722718 rad
∠ C' = γ' = 105.6333357081° = 105°38' = 1.29879427726 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 = 21 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 21+22+26 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-21)(34.5-22)(34.5-26) } ; ; T = sqrt{ 49485.94 } = 222.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 222.45 }{ 21 } = 21.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 222.45 }{ 22 } = 20.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 222.45 }{ 26 } = 17.11 ; ;

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{ 21**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 51° 3'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 54° 34'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-21**2-22**2 }{ 2 * 22 * 21 } ) = 74° 22' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 222.45 }{ 34.5 } = 6.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 51° 3'39" } = 13.5 ; ;




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