9 13 20 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 13   c = 20

Area: T = 44.98998886413
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 20.20552235834° = 20°12'19″ = 0.35326476776 rad
Angle ∠ B = β = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ C = γ = 129.868834155° = 129°52'6″ = 2.26766301542 rad

Height: ha = 9.97877530314
Height: hb = 6.90876751756
Height: hc = 4.49899888641

Median: ma = 16.2565768207
Median: mb = 14.08801278403
Median: mc = 5

Inradius: r = 2.13880899353
Circumradius: R = 13.02989855432

Vertex coordinates: A[20; 0] B[0; 0] C[7.8; 4.49899888641]
Centroid: CG[9.26766666667; 1.49766629547]
Coordinates of the circumscribed circle: U[10; -8.35219138098]
Coordinates of the inscribed circle: I[8; 2.13880899353]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7954776417° = 159°47'41″ = 0.35326476776 rad
∠ B' = β' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ C' = γ' = 50.132165845° = 50°7'54″ = 2.26766301542 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 = 9 ; ; b = 13 ; ; c = 20 ; ;

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

p = a+b+c = 9+13+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 * (21-9)(21-13)(21-20) } ; ; T = sqrt{ 2016 } = 44.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.9 }{ 9 } = 9.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.9 }{ 13 } = 6.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.9 }{ 20 } = 4.49 ; ;

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{ 9**2-13**2-20**2 }{ 2 * 13 * 20 } ) = 20° 12'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-9**2-20**2 }{ 2 * 9 * 20 } ) = 29° 55'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-9**2-13**2 }{ 2 * 13 * 9 } ) = 129° 52'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.9 }{ 21 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 12'19" } = 13.03 ; ;




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

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