8 27 30 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 27   c = 30

Area: T = 104.6354781502
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 14.97326234226° = 14°58'21″ = 0.26113215764 rad
Angle ∠ B = β = 60.68768010358° = 60°41'12″ = 1.05991844906 rad
Angle ∠ C = γ = 104.3410575542° = 104°20'26″ = 1.82110865866 rad

Height: ha = 26.15986953755
Height: hb = 7.75107245557
Height: hc = 6.97656521001

Median: ma = 28.25877423019
Median: mb = 17.31332896932
Median: mc = 13.09658008537

Inradius: r = 3.22195317385
Circumradius: R = 15.48224234996

Vertex coordinates: A[30; 0] B[0; 0] C[3.91766666667; 6.97656521001]
Centroid: CG[11.30655555556; 2.32552173667]
Coordinates of the circumscribed circle: U[15; -3.83547669316]
Coordinates of the inscribed circle: I[5.5; 3.22195317385]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.0277376577° = 165°1'39″ = 0.26113215764 rad
∠ B' = β' = 119.3133198964° = 119°18'48″ = 1.05991844906 rad
∠ C' = γ' = 75.65994244584° = 75°39'34″ = 1.82110865866 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 = 8 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 8+27+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-8)(32.5-27)(32.5-30) } ; ; T = sqrt{ 10948.44 } = 104.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.63 }{ 8 } = 26.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.63 }{ 27 } = 7.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.63 }{ 30 } = 6.98 ; ;

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{ 8**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 14° 58'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 60° 41'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-27**2 }{ 2 * 27 * 8 } ) = 104° 20'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.63 }{ 32.5 } = 3.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 58'21" } = 15.48 ; ;




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

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