Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10   b = 15.25   c = 7.64

Area: T = 33.39546604916
Perimeter: p = 32.89
Semiperimeter: s = 16.445

Angle ∠ A = α = 34.97771486016° = 34°58'38″ = 0.61104664061 rad
Angle ∠ B = β = 119.0498882075° = 119°2'56″ = 2.0787794963 rad
Angle ∠ C = γ = 25.97439693238° = 25°58'26″ = 0.45333312845 rad

Height: ha = 6.67989320983
Height: hb = 4.38796276055
Height: hc = 8.74220577203

Median: ma = 10.9765702711
Median: mb = 4.58773930505
Median: mc = 12.31662027427

Inradius: r = 2.03106877769
Circumradius: R = 8.72222027627

Vertex coordinates: A[7.64; 0] B[0; 0] C[-4.85655562827; 8.74220577203]
Centroid: CG[0.92881479058; 2.91440192401]
Coordinates of the circumscribed circle: U[3.82; 7.84112002292]
Coordinates of the inscribed circle: I[1.195; 2.03106877769]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0232851398° = 145°1'22″ = 0.61104664061 rad
∠ B' = β' = 60.95111179254° = 60°57'4″ = 2.0787794963 rad
∠ C' = γ' = 154.0266030676° = 154°1'34″ = 0.45333312845 rad

Calculate another triangle




How did we calculate this triangle?

a = 10 ; ; b = 15.25 ; ; c = 7.64 ; ;

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

p = a+b+c = 10+15.25+7.64 = 32.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.89 }{ 2 } = 16.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.45 * (16.45-10)(16.45-15.25)(16.45-7.64) } ; ; T = sqrt{ 1115.2 } = 33.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.39 }{ 10 } = 6.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.39 }{ 15.25 } = 4.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.39 }{ 7.64 } = 8.74 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 15.25**2+7.64**2-10**2 }{ 2 * 15.25 * 7.64 } ) = 34° 58'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+7.64**2-15.25**2 }{ 2 * 10 * 7.64 } ) = 119° 2'56" ; ; gamma = 180° - alpha - beta = 180° - 34° 58'38" - 119° 2'56" = 25° 58'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.39 }{ 16.45 } = 2.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 34° 58'38" } = 8.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 7.64**2 - 10**2 } }{ 2 } = 10.976 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.64**2+2 * 10**2 - 15.25**2 } }{ 2 } = 4.587 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 10**2 - 7.64**2 } }{ 2 } = 12.316 ; ;
Calculate another triangle

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

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