10 12 20 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 20

Area: T = 45.59660524607
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 27.12767531173° = 27°7'36″ = 0.47334511573 rad
Angle ∠ C = γ = 130.5421601874° = 130°32'30″ = 2.27883807635 rad

Height: ha = 9.11992104921
Height: hb = 7.59993420768
Height: hc = 4.56596052461

Median: ma = 15.71662336455
Median: mb = 14.62987388383
Median: mc = 4.69904157598

Inradius: r = 2.17112405934
Circumradius: R = 13.15990338992

Vertex coordinates: A[20; 0] B[0; 0] C[8.9; 4.56596052461]
Centroid: CG[9.63333333333; 1.52198684154]
Coordinates of the circumscribed circle: U[10; -8.55333720345]
Coordinates of the inscribed circle: I[9; 2.17112405934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 152.8733246883° = 152°52'24″ = 0.47334511573 rad
∠ C' = γ' = 49.45883981265° = 49°27'30″ = 2.27883807635 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 = 10 ; ; b = 12 ; ; c = 20 ; ;

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

p = a+b+c = 10+12+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-10)(21-12)(21-20) } ; ; T = sqrt{ 2079 } = 45.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.6 }{ 10 } = 9.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.6 }{ 12 } = 7.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.6 }{ 20 } = 4.56 ; ;

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{ 10**2-12**2-20**2 }{ 2 * 12 * 20 } ) = 22° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-10**2-20**2 }{ 2 * 10 * 20 } ) = 27° 7'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-10**2-12**2 }{ 2 * 12 * 10 } ) = 130° 32'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.6 }{ 21 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 19'54" } = 13.16 ; ;




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

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