9 18 25 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 18   c = 25

Area: T = 59.46442749893
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 15.32545113215° = 15°19'28″ = 0.26774631788 rad
Angle ∠ B = β = 31.90989763008° = 31°54'32″ = 0.55769166974 rad
Angle ∠ C = γ = 132.7676512378° = 132°45'59″ = 2.31772127774 rad

Height: ha = 13.21442833309
Height: hb = 6.60771416655
Height: hc = 4.75771419991

Median: ma = 21.31331414859
Median: mb = 16.49224225025
Median: mc = 6.80107352544

Inradius: r = 2.28770874996
Circumradius: R = 17.0277030098

Vertex coordinates: A[25; 0] B[0; 0] C[7.64; 4.75771419991]
Centroid: CG[10.88; 1.58657139997]
Coordinates of the circumscribed circle: U[12.5; -11.56215636468]
Coordinates of the inscribed circle: I[8; 2.28770874996]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6755488678° = 164°40'32″ = 0.26774631788 rad
∠ B' = β' = 148.0911023699° = 148°5'28″ = 0.55769166974 rad
∠ C' = γ' = 47.23334876223° = 47°14'1″ = 2.31772127774 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 = 9 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 9+18+25 = 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 * (26-9)(26-18)(26-25) } ; ; T = sqrt{ 3536 } = 59.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.46 }{ 9 } = 13.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.46 }{ 18 } = 6.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.46 }{ 25 } = 4.76 ; ;

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{ 9**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 15° 19'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 31° 54'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-18**2 }{ 2 * 18 * 9 } ) = 132° 45'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.46 }{ 26 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 15° 19'28" } = 17.03 ; ;




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

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