13 19 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 19   c = 25

Area: T = 121.1954832811
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 30.6833417109° = 30°41' = 0.53655266543 rad
Angle ∠ B = β = 48.22990936801° = 48°13'45″ = 0.842175648 rad
Angle ∠ C = γ = 101.0877489211° = 101°5'15″ = 1.76443095193 rad

Height: ha = 18.64553588939
Height: hb = 12.75773508222
Height: hc = 9.69655866249

Median: ma = 21.23108737456
Median: mb = 17.51442798881
Median: mc = 10.42883268073

Inradius: r = 4.25224502741
Circumradius: R = 12.73877542771

Vertex coordinates: A[25; 0] B[0; 0] C[8.66; 9.69655866249]
Centroid: CG[11.22; 3.23218622083]
Coordinates of the circumscribed circle: U[12.5; -2.45495681302]
Coordinates of the inscribed circle: I[9.5; 4.25224502741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.3176582891° = 149°19' = 0.53655266543 rad
∠ B' = β' = 131.771090632° = 131°46'15″ = 0.842175648 rad
∠ C' = γ' = 78.9132510789° = 78°54'45″ = 1.76443095193 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 = 25 ; ;

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

p = a+b+c = 13+19+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-13)(28.5-19)(28.5-25) } ; ; T = sqrt{ 14688.19 } = 121.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 121.19 }{ 13 } = 18.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 121.19 }{ 19 } = 12.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 121.19 }{ 25 } = 9.7 ; ;

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**2-25**2 }{ 2 * 19 * 25 } ) = 30° 41' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 48° 13'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-19**2 }{ 2 * 19 * 13 } ) = 101° 5'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 121.19 }{ 28.5 } = 4.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 30° 41' } = 12.74 ; ;




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

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