16 21 26 triangle

Acute scalene triangle.

Sides: a = 16   b = 21   c = 26

Area: T = 167.9187948713
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 37.95880285807° = 37°57'29″ = 0.66224925763 rad
Angle ∠ B = β = 53.83327560786° = 53°49'58″ = 0.9439558839 rad
Angle ∠ C = γ = 88.20992153407° = 88°12'33″ = 1.54395412383 rad

Height: ha = 20.99897435891
Height: hb = 15.99221855917
Height: hc = 12.91767652856

Median: ma = 22.23773559579
Median: mb = 18.86113361139
Median: mc = 13.3987761007

Inradius: r = 5.33107285306
Circumradius: R = 13.00663523092

Vertex coordinates: A[26; 0] B[0; 0] C[9.44223076923; 12.91767652856]
Centroid: CG[11.81441025641; 4.30655884285]
Coordinates of the circumscribed circle: U[13; 0.40664485097]
Coordinates of the inscribed circle: I[10.5; 5.33107285306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0421971419° = 142°2'31″ = 0.66224925763 rad
∠ B' = β' = 126.1677243921° = 126°10'2″ = 0.9439558839 rad
∠ C' = γ' = 91.79107846593° = 91°47'27″ = 1.54395412383 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 = 16 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 16+21+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-16)(31.5-21)(31.5-26) } ; ; T = sqrt{ 28196.44 } = 167.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 167.92 }{ 16 } = 20.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 167.92 }{ 21 } = 15.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 167.92 }{ 26 } = 12.92 ; ;

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{ 16**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 37° 57'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 53° 49'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-21**2 }{ 2 * 21 * 16 } ) = 88° 12'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 167.92 }{ 31.5 } = 5.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 57'29" } = 13.01 ; ;




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