13 24 27 triangle

Acute scalene triangle.

Sides: a = 13   b = 24   c = 27

Area: T = 155.9498709517
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 28.77218565328° = 28°46'19″ = 0.50221636284 rad
Angle ∠ B = β = 62.69774270485° = 62°41'51″ = 1.09442765345 rad
Angle ∠ C = γ = 88.53107164186° = 88°31'51″ = 1.54551524907 rad

Height: ha = 23.99221091565
Height: hb = 12.99657257931
Height: hc = 11.55217562605

Median: ma = 24.70332386541
Median: mb = 17.46442491966
Median: mc = 13.79331142241

Inradius: r = 4.87333971724
Circumradius: R = 13.50444400593

Vertex coordinates: A[27; 0] B[0; 0] C[5.9632962963; 11.55217562605]
Centroid: CG[10.9887654321; 3.85105854202]
Coordinates of the circumscribed circle: U[13.5; 0.34662676938]
Coordinates of the inscribed circle: I[8; 4.87333971724]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.2288143467° = 151°13'41″ = 0.50221636284 rad
∠ B' = β' = 117.3032572951° = 117°18'9″ = 1.09442765345 rad
∠ C' = γ' = 91.46992835814° = 91°28'9″ = 1.54551524907 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 = 13 ; ; b = 24 ; ; c = 27 ; ;

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

p = a+b+c = 13+24+27 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-13)(32-24)(32-27) } ; ; T = sqrt{ 24320 } = 155.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 155.95 }{ 13 } = 23.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 155.95 }{ 24 } = 13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 155.95 }{ 27 } = 11.55 ; ;

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{ 13**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 28° 46'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-13**2-27**2 }{ 2 * 13 * 27 } ) = 62° 41'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-13**2-24**2 }{ 2 * 24 * 13 } ) = 88° 31'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 155.95 }{ 32 } = 4.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 28° 46'19" } = 13.5 ; ;




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

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