20 25 26 triangle

Acute scalene triangle.

Sides: a = 20   b = 25   c = 26

Area: T = 234.2810681022
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 46.1265829757° = 46°7'33″ = 0.80550475995 rad
Angle ∠ B = β = 64.330033309° = 64°18'1″ = 1.12222525225 rad
Angle ∠ C = γ = 69.5743837153° = 69°34'26″ = 1.21442925316 rad

Height: ha = 23.42880681022
Height: hb = 18.74224544817
Height: hc = 18.02215908478

Median: ma = 23.46327364133
Median: mb = 19.53884236826
Median: mc = 18.53437529929

Inradius: r = 6.59994558034
Circumradius: R = 13.87222492432

Vertex coordinates: A[26; 0] B[0; 0] C[8.67330769231; 18.02215908478]
Centroid: CG[11.55876923077; 6.00771969493]
Coordinates of the circumscribed circle: U[13; 4.84114149859]
Coordinates of the inscribed circle: I[10.5; 6.59994558034]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.8744170243° = 133°52'27″ = 0.80550475995 rad
∠ B' = β' = 115.769966691° = 115°41'59″ = 1.12222525225 rad
∠ C' = γ' = 110.4266162847° = 110°25'34″ = 1.21442925316 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 = 20 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 20+25+26 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-20)(35.5-25)(35.5-26) } ; ; T = sqrt{ 54887.44 } = 234.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.28 }{ 20 } = 23.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.28 }{ 25 } = 18.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.28 }{ 26 } = 18.02 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 25**2+26**2-20**2 }{ 2 * 25 * 26 } ) = 46° 7'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+26**2-25**2 }{ 2 * 20 * 26 } ) = 64° 18'1" ; ; gamma = 180° - alpha - beta = 180° - 46° 7'33" - 64° 18'1" = 69° 34'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.28 }{ 35.5 } = 6.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 46° 7'33" } = 13.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 26**2 - 20**2 } }{ 2 } = 23.463 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 20**2 - 25**2 } }{ 2 } = 19.538 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 20**2 - 26**2 } }{ 2 } = 18.534 ; ;
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