6 24 27 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 27

Area: T = 65.79108618275
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 21.93302872758
Height: hb = 5.4832571819
Height: hc = 4.87333971724

Median: ma = 25.36773017879
Median: mb = 15.44334452115
Median: mc = 11.12442977306

Inradius: r = 2.30884512922
Circumradius: R = 14.774408827

Vertex coordinates: A[27; 0] B[0; 0] C[3.5; 4.87333971724]
Centroid: CG[10.16766666667; 1.62444657241]
Coordinates of the circumscribed circle: U[13.5; -6.00219733597]
Coordinates of the inscribed circle: I[4.5; 2.30884512922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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 = 6 ; ; b = 24 ; ; c = 27 ; ;

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

p = a+b+c = 6+24+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-6)(28.5-24)(28.5-27) } ; ; T = sqrt{ 4328.44 } = 65.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.79 }{ 6 } = 21.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.79 }{ 24 } = 5.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.79 }{ 27 } = 4.87 ; ;

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{ 6**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 11° 42'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-6**2-27**2 }{ 2 * 6 * 27 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-6**2-24**2 }{ 2 * 24 * 6 } ) = 113° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.79 }{ 28.5 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 42'57" } = 14.77 ; ;




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

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