Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 8   b = 12   c = 14

Area: T = 47.9066158268
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 86.41766783015° = 86°25' = 1.5088255565 rad

Height: ha = 11.9776539567
Height: hb = 7.98443597113
Height: hc = 6.84437368954

Median: ma = 12.4109673646
Median: mb = 9.69553597148
Median: mc = 7.41661984871

Inradius: r = 2.81880093099
Circumradius: R = 7.01437120602

Vertex coordinates: A[14; 0] B[0; 0] C[4.14328571429; 6.84437368954]
Centroid: CG[6.04876190476; 2.28112456318]
Coordinates of the circumscribed circle: U[7; 0.43883570038]
Coordinates of the inscribed circle: I[5; 2.81880093099]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 93.58333216985° = 93°35' = 1.5088255565 rad

Calculate another triangle




How did we calculate this triangle?

a = 8 ; ; b = 12 ; ; c = 14 ; ;

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

p = a+b+c = 8+12+14 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-8)(17-12)(17-14) } ; ; T = sqrt{ 2295 } = 47.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.91 }{ 8 } = 11.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.91 }{ 12 } = 7.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.91 }{ 14 } = 6.84 ; ;

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{ 12**2+14**2-8**2 }{ 2 * 12 * 14 } ) = 34° 46'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+14**2-12**2 }{ 2 * 8 * 14 } ) = 58° 48'41" ; ; gamma = 180° - alpha - beta = 180° - 34° 46'19" - 58° 48'41" = 86° 25' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.91 }{ 17 } = 2.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 34° 46'19" } = 7.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 14**2 - 8**2 } }{ 2 } = 12.41 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 8**2 - 12**2 } }{ 2 } = 9.695 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 8**2 - 14**2 } }{ 2 } = 7.416 ; ;
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.