Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12   b = 24   c = 25

Area: T = 142.0287946194
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 28.25769481283° = 28°15'25″ = 0.49331767814 rad
Angle ∠ B = β = 71.23662521963° = 71°14'10″ = 1.24333071476 rad
Angle ∠ C = γ = 80.50767996754° = 80°30'24″ = 1.40551087246 rad

Height: ha = 23.67113243656
Height: hb = 11.83656621828
Height: hc = 11.36222356955

Median: ma = 23.7599208741
Median: mb = 15.50880624193
Median: mc = 14.27441024236

Inradius: r = 4.65766539736
Circumradius: R = 12.6743562128

Vertex coordinates: A[25; 0] B[0; 0] C[3.86; 11.36222356955]
Centroid: CG[9.62; 3.78774118985]
Coordinates of the circumscribed circle: U[12.5; 2.09902576426]
Coordinates of the inscribed circle: I[6.5; 4.65766539736]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.7433051872° = 151°44'35″ = 0.49331767814 rad
∠ B' = β' = 108.7643747804° = 108°45'49″ = 1.24333071476 rad
∠ C' = γ' = 99.49332003246° = 99°29'36″ = 1.40551087246 rad

Calculate another triangle




How did we calculate this triangle?

a = 12 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 12+24+25 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-12)(30.5-24)(30.5-25) } ; ; T = sqrt{ 20171.94 } = 142.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.03 }{ 12 } = 23.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.03 }{ 24 } = 11.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.03 }{ 25 } = 11.36 ; ;

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{ 12**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 28° 15'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 71° 14'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-24**2 }{ 2 * 24 * 12 } ) = 80° 30'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.03 }{ 30.5 } = 4.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 28° 15'25" } = 12.67 ; ;

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

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