9 13 19 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 13   c = 19

Area: T = 51.49993932003
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 24.64552747866° = 24°38'43″ = 0.43301411901 rad
Angle ∠ B = β = 37.03771040964° = 37°2'14″ = 0.64664194119 rad
Angle ∠ C = γ = 118.3187621117° = 118°19'3″ = 2.06550320516 rad

Height: ha = 11.44443096001
Height: hb = 7.92329835693
Height: hc = 5.42109887579

Median: ma = 15.64444878472
Median: mb = 13.37697419571
Median: mc = 5.89549130613

Inradius: r = 2.5122165522
Circumradius: R = 10.79113892857

Vertex coordinates: A[19; 0] B[0; 0] C[7.18442105263; 5.42109887579]
Centroid: CG[8.72880701754; 1.80769962526]
Coordinates of the circumscribed circle: U[9.5; -5.11989923535]
Coordinates of the inscribed circle: I[7.5; 2.5122165522]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3554725213° = 155°21'17″ = 0.43301411901 rad
∠ B' = β' = 142.9632895904° = 142°57'46″ = 0.64664194119 rad
∠ C' = γ' = 61.6822378883° = 61°40'57″ = 2.06550320516 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 = 19 ; ;

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

p = a+b+c = 9+13+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-9)(20.5-13)(20.5-19) } ; ; T = sqrt{ 2652.19 } = 51.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.5 }{ 9 } = 11.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.5 }{ 13 } = 7.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.5 }{ 19 } = 5.42 ; ;

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**2-19**2 }{ 2 * 13 * 19 } ) = 24° 38'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-9**2-19**2 }{ 2 * 9 * 19 } ) = 37° 2'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-9**2-13**2 }{ 2 * 13 * 9 } ) = 118° 19'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.5 }{ 20.5 } = 2.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 24° 38'43" } = 10.79 ; ;




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

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