8 22 25 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 22   c = 25

Area: T = 85.8698722478
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 59.17695025682° = 59°10'10″ = 1.03327026366 rad
Angle ∠ C = γ = 102.6365625093° = 102°38'8″ = 1.79113295877 rad

Height: ha = 21.46771806195
Height: hb = 7.8066247498
Height: hc = 6.86994977982

Median: ma = 23.20656027717
Median: mb = 14.95499163877
Median: mc = 10.85112672071

Inradius: r = 3.12224989992
Circumradius: R = 12.81102523044

Vertex coordinates: A[25; 0] B[0; 0] C[4.1; 6.86994977982]
Centroid: CG[9.7; 2.29898325994]
Coordinates of the circumscribed circle: U[12.5; -2.80222426916]
Coordinates of the inscribed circle: I[5.5; 3.12224989992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 120.8330497432° = 120°49'50″ = 1.03327026366 rad
∠ C' = γ' = 77.3644374907° = 77°21'52″ = 1.79113295877 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 = 22 ; ; c = 25 ; ;

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

p = a+b+c = 8+22+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-8)(27.5-22)(27.5-25) } ; ; T = sqrt{ 7373.44 } = 85.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 85.87 }{ 8 } = 21.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 85.87 }{ 22 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 85.87 }{ 25 } = 6.87 ; ;

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**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 59° 10'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 102° 38'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 85.87 }{ 27.5 } = 3.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 11'42" } = 12.81 ; ;




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

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