11 12 13 triangle

Acute scalene triangle.

Sides: a = 11   b = 12   c = 13

Area: T = 61.48217045958
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 52.02201275551° = 52°1'12″ = 0.90879225031 rad
Angle ∠ B = β = 59.30435587083° = 59°18'13″ = 1.03550423576 rad
Angle ∠ C = γ = 68.67663137365° = 68°40'35″ = 1.19986277928 rad

Height: ha = 11.17884917447
Height: hb = 10.2476950766
Height: hc = 9.4598723784

Median: ma = 11.23661025271
Median: mb = 10.44403065089
Median: mc = 9.5

Inradius: r = 3.41656502553
Circumradius: R = 6.97876855216

Vertex coordinates: A[13; 0] B[0; 0] C[5.61553846154; 9.4598723784]
Centroid: CG[6.20551282051; 3.1532907928]
Coordinates of the circumscribed circle: U[6.5; 2.53773401897]
Coordinates of the inscribed circle: I[6; 3.41656502553]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.9879872445° = 127°58'48″ = 0.90879225031 rad
∠ B' = β' = 120.6966441292° = 120°41'47″ = 1.03550423576 rad
∠ C' = γ' = 111.3243686263° = 111°19'25″ = 1.19986277928 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 = 11 ; ; b = 12 ; ; c = 13 ; ;

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

p = a+b+c = 11+12+13 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-11)(18-12)(18-13) } ; ; T = sqrt{ 3780 } = 61.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.48 }{ 11 } = 11.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.48 }{ 12 } = 10.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.48 }{ 13 } = 9.46 ; ;

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{ 11**2-12**2-13**2 }{ 2 * 12 * 13 } ) = 52° 1'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 59° 18'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 68° 40'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.48 }{ 18 } = 3.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 52° 1'12" } = 6.98 ; ;




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

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