6 24 25 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 25

Area: T = 71.92766119041
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 13.8722102735° = 13°52'20″ = 0.24221138669 rad
Angle ∠ B = β = 73.54107503717° = 73°32'27″ = 1.28435282284 rad
Angle ∠ C = γ = 92.58771468932° = 92°35'14″ = 1.61659505583 rad

Height: ha = 23.97655373014
Height: hb = 5.99438843253
Height: hc = 5.75441289523

Median: ma = 24.3210773014
Median: mb = 13.65765002837
Median: mc = 12.23772382505

Inradius: r = 2.61655131601
Circumradius: R = 12.51327539887

Vertex coordinates: A[25; 0] B[0; 0] C[1.7; 5.75441289523]
Centroid: CG[8.9; 1.91880429841]
Coordinates of the circumscribed circle: U[12.5; -0.5654811812]
Coordinates of the inscribed circle: I[3.5; 2.61655131601]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1287897265° = 166°7'40″ = 0.24221138669 rad
∠ B' = β' = 106.4599249628° = 106°27'33″ = 1.28435282284 rad
∠ C' = γ' = 87.41328531068° = 87°24'46″ = 1.61659505583 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 = 6 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 6+24+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 * (27.5-6)(27.5-24)(27.5-25) } ; ; T = sqrt{ 5173.44 } = 71.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.93 }{ 6 } = 23.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.93 }{ 24 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.93 }{ 25 } = 5.75 ; ;

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{ 6**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 13° 52'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-6**2-25**2 }{ 2 * 6 * 25 } ) = 73° 32'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-6**2-24**2 }{ 2 * 24 * 6 } ) = 92° 35'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.93 }{ 27.5 } = 2.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 52'20" } = 12.51 ; ;




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

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