8 18 24 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 18   c = 24

Area: T = 54.54435605732
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 14.62664748646° = 14°37'35″ = 0.25552801443 rad
Angle ∠ B = β = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ C = γ = 130.7511363296° = 130°45'5″ = 2.2822041791 rad

Height: ha = 13.63658901433
Height: hb = 6.06603956192
Height: hc = 4.54552967144

Median: ma = 20.8332666656
Median: mb = 15.46596248337
Median: mc = 7.07110678119

Inradius: r = 2.18217424229
Circumradius: R = 15.84105500286

Vertex coordinates: A[24; 0] B[0; 0] C[6.58333333333; 4.54552967144]
Centroid: CG[10.19444444444; 1.51550989048]
Coordinates of the circumscribed circle: U[12; -10.34403590465]
Coordinates of the inscribed circle: I[7; 2.18217424229]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3743525135° = 165°22'25″ = 0.25552801443 rad
∠ B' = β' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ C' = γ' = 49.24986367043° = 49°14'55″ = 2.2822041791 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 = 8 ; ; b = 18 ; ; c = 24 ; ;

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

p = a+b+c = 8+18+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-8)(25-18)(25-24) } ; ; T = sqrt{ 2975 } = 54.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.54 }{ 8 } = 13.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.54 }{ 18 } = 6.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.54 }{ 24 } = 4.55 ; ;

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{ 8**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 14° 37'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-8**2-24**2 }{ 2 * 8 * 24 } ) = 34° 37'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-8**2-18**2 }{ 2 * 18 * 8 } ) = 130° 45'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.54 }{ 25 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 37'35" } = 15.84 ; ;




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

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