21 25 26 triangle

Acute scalene triangle.

Sides: a = 21   b = 25   c = 26

Area: T = 243.7211152139
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 48.58326895819° = 48°34'58″ = 0.84879278927 rad
Angle ∠ B = β = 63.22110584075° = 63°13'16″ = 1.10334156258 rad
Angle ∠ C = γ = 68.19662520106° = 68°11'47″ = 1.19902491351 rad

Height: ha = 23.2121538299
Height: hb = 19.49876921711
Height: hc = 18.74877809338

Median: ma = 23.24332785983
Median: mb = 20.05661711201
Median: mc = 19.07987840283

Inradius: r = 6.77700320039
Circumradius: R = 14.00216570989

Vertex coordinates: A[26; 0] B[0; 0] C[9.46215384615; 18.74877809338]
Centroid: CG[11.82105128205; 6.24992603113]
Coordinates of the circumscribed circle: U[13; 5.20106154939]
Coordinates of the inscribed circle: I[11; 6.77700320039]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.4177310418° = 131°25'2″ = 0.84879278927 rad
∠ B' = β' = 116.7798941592° = 116°46'44″ = 1.10334156258 rad
∠ C' = γ' = 111.8043747989° = 111°48'13″ = 1.19902491351 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 21+25+26 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-21)(36-25)(36-26) } ; ; T = sqrt{ 59400 } = 243.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 243.72 }{ 21 } = 23.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 243.72 }{ 25 } = 19.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 243.72 }{ 26 } = 18.75 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 48° 34'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 63° 13'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-21**2-25**2 }{ 2 * 25 * 21 } ) = 68° 11'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 243.72 }{ 36 } = 6.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 48° 34'58" } = 14 ; ;




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