13 24 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 24   c = 30

Area: T = 151.1110679636
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 24.81989241279° = 24°49'8″ = 0.43331719428 rad
Angle ∠ B = β = 50.79883749279° = 50°47'54″ = 0.88765988972 rad
Angle ∠ C = γ = 104.3832700944° = 104°22'58″ = 1.82218218136 rad

Height: ha = 23.2487796867
Height: hb = 12.59325566363
Height: hc = 10.07440453091

Median: ma = 26.37770733782
Median: mb = 19.76110728454
Median: mc = 12.14549578015

Inradius: r = 4.51107665563
Circumradius: R = 15.48553383337

Vertex coordinates: A[30; 0] B[0; 0] C[8.21766666667; 10.07440453091]
Centroid: CG[12.73988888889; 3.3588015103]
Coordinates of the circumscribed circle: U[15; -3.84765183361]
Coordinates of the inscribed circle: I[9.5; 4.51107665563]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1811075872° = 155°10'52″ = 0.43331719428 rad
∠ B' = β' = 129.2021625072° = 129°12'6″ = 0.88765988972 rad
∠ C' = γ' = 75.61772990558° = 75°37'2″ = 1.82218218136 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 = 24 ; ; c = 30 ; ;

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

p = a+b+c = 13+24+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-13)(33.5-24)(33.5-30) } ; ; T = sqrt{ 22834.44 } = 151.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.11 }{ 13 } = 23.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.11 }{ 24 } = 12.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.11 }{ 30 } = 10.07 ; ;

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**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 24° 49'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 50° 47'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-24**2 }{ 2 * 24 * 13 } ) = 104° 22'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.11 }{ 33.5 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 24° 49'8" } = 15.49 ; ;




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

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