13 19 20 triangle

Acute scalene triangle.

Sides: a = 13   b = 19   c = 20

Area: T = 119.1476968069
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 38.83657017687° = 38°50'9″ = 0.67878108632 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 74.74224767095° = 74°44'33″ = 1.30545023097 rad

Height: ha = 18.33303027798
Height: hb = 12.54217861125
Height: hc = 11.91546968069

Median: ma = 18.39215741577
Median: mb = 13.93773598648
Median: mc = 12.84552325787

Inradius: r = 4.5832575695
Circumradius: R = 10.36553497862

Vertex coordinates: A[20; 0] B[0; 0] C[5.2; 11.91546968069]
Centroid: CG[8.4; 3.97215656023]
Coordinates of the circumscribed circle: U[10; 2.72877236279]
Coordinates of the inscribed circle: I[7; 4.5832575695]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.1644298231° = 141°9'51″ = 0.67878108632 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 105.258752329° = 105°15'27″ = 1.30545023097 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 = 20 ; ;

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

p = a+b+c = 13+19+20 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-13)(26-19)(26-20) } ; ; T = sqrt{ 14196 } = 119.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.15 }{ 13 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.15 }{ 19 } = 12.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.15 }{ 20 } = 11.91 ; ;

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**2-20**2 }{ 2 * 19 * 20 } ) = 38° 50'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-13**2-20**2 }{ 2 * 13 * 20 } ) = 66° 25'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-13**2-19**2 }{ 2 * 19 * 13 } ) = 74° 44'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.15 }{ 26 } = 4.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 38° 50'9" } = 10.37 ; ;




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

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