21 23 27 triangle

Acute scalene triangle.

Sides: a = 21   b = 23   c = 27

Area: T = 233.8643608755
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 48.86769371798° = 48°52'1″ = 0.85328889492 rad
Angle ∠ B = β = 55.58799483259° = 55°34'48″ = 0.97700530964 rad
Angle ∠ C = γ = 75.55331144943° = 75°33'11″ = 1.31986506081 rad

Height: ha = 22.27327246434
Height: hb = 20.33659659787
Height: hc = 17.32332302782

Median: ma = 22.77660839479
Median: mb = 21.2787922831
Median: mc = 17.43997126413

Inradius: r = 6.58877072889
Circumradius: R = 13.94108179723

Vertex coordinates: A[27; 0] B[0; 0] C[11.87703703704; 17.32332302782]
Centroid: CG[12.95767901235; 5.77444100927]
Coordinates of the circumscribed circle: U[13.5; 3.47879887488]
Coordinates of the inscribed circle: I[12.5; 6.58877072889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.133306282° = 131°7'59″ = 0.85328889492 rad
∠ B' = β' = 124.4220051674° = 124°25'12″ = 0.97700530964 rad
∠ C' = γ' = 104.4476885506° = 104°26'49″ = 1.31986506081 rad

Calculate another triangle




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 = 23 ; ; c = 27 ; ;

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

p = a+b+c = 21+23+27 = 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 * (35.5-21)(35.5-23)(35.5-27) } ; ; T = sqrt{ 54692.19 } = 233.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 233.86 }{ 21 } = 22.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 233.86 }{ 23 } = 20.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 233.86 }{ 27 } = 17.32 ; ;

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**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 48° 52'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-21**2-27**2 }{ 2 * 21 * 27 } ) = 55° 34'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-21**2-23**2 }{ 2 * 23 * 21 } ) = 75° 33'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 233.86 }{ 35.5 } = 6.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 48° 52'1" } = 13.94 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.