13 19 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 19   c = 30

Area: T = 81.82990901819
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 16.68655898881° = 16°41'8″ = 0.29112184812 rad
Angle ∠ B = β = 24.81216315026° = 24°48'42″ = 0.43330446625 rad
Angle ∠ C = γ = 138.5032778609° = 138°30'10″ = 2.41773295099 rad

Height: ha = 12.58990907972
Height: hb = 8.61435884402
Height: hc = 5.45552726788

Median: ma = 24.25438656713
Median: mb = 21.07772389084
Median: mc = 6.32545553203

Inradius: r = 2.64396480704
Circumradius: R = 22.63986483814

Vertex coordinates: A[30; 0] B[0; 0] C[11.8; 5.45552726788]
Centroid: CG[13.93333333333; 1.81884242263]
Coordinates of the circumscribed circle: U[15; -16.95660726743]
Coordinates of the inscribed circle: I[12; 2.64396480704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.3144410112° = 163°18'52″ = 0.29112184812 rad
∠ B' = β' = 155.1888368497° = 155°11'18″ = 0.43330446625 rad
∠ C' = γ' = 41.49772213907° = 41°29'50″ = 2.41773295099 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 = 13 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 13+19+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-13)(31-19)(31-30) } ; ; T = sqrt{ 6696 } = 81.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.83 }{ 13 } = 12.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.83 }{ 19 } = 8.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.83 }{ 30 } = 5.46 ; ;

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{ 13**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 16° 41'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 24° 48'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-19**2 }{ 2 * 19 * 13 } ) = 138° 30'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.83 }{ 31 } = 2.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 16° 41'8" } = 22.64 ; ;




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

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