11 12 21 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 12   c = 21

Area: T = 49.1933495505
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 22.98109198075° = 22°58'51″ = 0.40110927158 rad
Angle ∠ B = β = 25.20987652968° = 25°12'32″ = 0.44399759548 rad
Angle ∠ C = γ = 131.8110314896° = 131°48'37″ = 2.3010523983 rad

Height: ha = 8.944427191
Height: hb = 8.19989159175
Height: hc = 4.685509481

Median: ma = 16.19441347407
Median: mb = 15.65224758425
Median: mc = 4.7176990566

Inradius: r = 2.23660679775
Circumradius: R = 14.08772282582

Vertex coordinates: A[21; 0] B[0; 0] C[9.95223809524; 4.685509481]
Centroid: CG[10.31774603175; 1.562169827]
Coordinates of the circumscribed circle: U[10.5; -9.39114855055]
Coordinates of the inscribed circle: I[10; 2.23660679775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.0199080193° = 157°1'9″ = 0.40110927158 rad
∠ B' = β' = 154.7911234703° = 154°47'28″ = 0.44399759548 rad
∠ C' = γ' = 48.19896851042° = 48°11'23″ = 2.3010523983 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 = 21 ; ;

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

p = a+b+c = 11+12+21 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-11)(22-12)(22-21) } ; ; T = sqrt{ 2420 } = 49.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.19 }{ 11 } = 8.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.19 }{ 12 } = 8.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.19 }{ 21 } = 4.69 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 12**2+21**2-11**2 }{ 2 * 12 * 21 } ) = 22° 58'51" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+21**2-12**2 }{ 2 * 11 * 21 } ) = 25° 12'32" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 11**2+12**2-21**2 }{ 2 * 11 * 12 } ) = 131° 48'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.19 }{ 22 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 58'51" } = 14.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 21**2 - 11**2 } }{ 2 } = 16.194 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 11**2 - 12**2 } }{ 2 } = 15.652 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 11**2 - 21**2 } }{ 2 } = 4.717 ; ;
Calculate another triangle

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

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