13 16 24 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 24

Area: T = 96.90768496031
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 30.31329778294° = 30°18'47″ = 0.52990612692 rad
Angle ∠ B = β = 38.40436536582° = 38°24'13″ = 0.67702702011 rad
Angle ∠ C = γ = 111.2833368512° = 111°17' = 1.94222611833 rad

Height: ha = 14.90987460928
Height: hb = 12.11333562004
Height: hc = 8.07655708003

Median: ma = 19.33326149292
Median: mb = 17.56441680703
Median: mc = 8.27664726786

Inradius: r = 3.65768622492
Circumradius: R = 12.87883466299

Vertex coordinates: A[24; 0] B[0; 0] C[10.18875; 8.07655708003]
Centroid: CG[11.39658333333; 2.69218569334]
Coordinates of the circumscribed circle: U[12; -4.67545921661]
Coordinates of the inscribed circle: I[10.5; 3.65768622492]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.6877022171° = 149°41'13″ = 0.52990612692 rad
∠ B' = β' = 141.5966346342° = 141°35'47″ = 0.67702702011 rad
∠ C' = γ' = 68.71766314876° = 68°43' = 1.94222611833 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 = 16 ; ; c = 24 ; ;

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

p = a+b+c = 13+16+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-13)(26.5-16)(26.5-24) } ; ; T = sqrt{ 9390.94 } = 96.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 96.91 }{ 13 } = 14.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96.91 }{ 16 } = 12.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96.91 }{ 24 } = 8.08 ; ;

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**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 30° 18'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-24**2 }{ 2 * 13 * 24 } ) = 38° 24'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 111° 17' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96.91 }{ 26.5 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 30° 18'47" } = 12.88 ; ;




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

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