13 15 24 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 15   c = 24

Area: T = 86.23222445492
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 28.62545509534° = 28°37'28″ = 0.5499592661 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 117.8188139285° = 117°49'5″ = 2.05663144491 rad

Height: ha = 13.26664991614
Height: hb = 11.49876326066
Height: hc = 7.18660203791

Median: ma = 18.92774932307
Median: mb = 17.78334192438
Median: mc = 7.28801098893

Inradius: r = 3.31766247904
Circumradius: R = 13.5688010506

Vertex coordinates: A[24; 0] B[0; 0] C[10.83333333333; 7.18660203791]
Centroid: CG[11.61111111111; 2.39553401264]
Coordinates of the circumscribed circle: U[12; -6.33217382361]
Coordinates of the inscribed circle: I[11; 3.31766247904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3755449047° = 151°22'32″ = 0.5499592661 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 62.18218607153° = 62°10'55″ = 2.05663144491 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 = 15 ; ; c = 24 ; ;

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

p = a+b+c = 13+15+24 = 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)(26-15)(26-24) } ; ; T = sqrt{ 7436 } = 86.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.23 }{ 13 } = 13.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.23 }{ 15 } = 11.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.23 }{ 24 } = 7.19 ; ;

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**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 28° 37'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-13**2-24**2 }{ 2 * 13 * 24 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-13**2-15**2 }{ 2 * 15 * 13 } ) = 117° 49'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.23 }{ 26 } = 3.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 28° 37'28" } = 13.57 ; ;




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

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