Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 17

Area: T = 58.93658761706
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 35.2966144734° = 35°17'46″ = 0.61660339389 rad
Angle ∠ B = β = 43.89769323912° = 43°53'49″ = 0.76661460018 rad
Angle ∠ C = γ = 100.8076922875° = 100°48'25″ = 1.7599412713 rad

Height: ha = 11.78771752341
Height: hb = 9.82326460284
Height: hc = 6.93436324907

Median: ma = 13.83883525031
Median: mb = 12.5989678312
Median: mc = 7.05333679898

Inradius: r = 3.02223526241
Circumradius: R = 8.65334727765

Vertex coordinates: A[17; 0] B[0; 0] C[7.20658823529; 6.93436324907]
Centroid: CG[8.0698627451; 2.31112108302]
Coordinates of the circumscribed circle: U[8.5; -1.62325261456]
Coordinates of the inscribed circle: I[7.5; 3.02223526241]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7043855266° = 144°42'14″ = 0.61660339389 rad
∠ B' = β' = 136.1033067609° = 136°6'11″ = 0.76661460018 rad
∠ C' = γ' = 79.19330771251° = 79°11'35″ = 1.7599412713 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 10+12+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-10)(19.5-12)(19.5-17) } ; ; T = sqrt{ 3473.44 } = 58.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.94 }{ 10 } = 11.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.94 }{ 12 } = 9.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.94 }{ 17 } = 6.93 ; ;

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+17**2-10**2 }{ 2 * 12 * 17 } ) = 35° 17'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+17**2-12**2 }{ 2 * 10 * 17 } ) = 43° 53'49" ; ;
 gamma = 180° - alpha - beta = 180° - 35° 17'46" - 43° 53'49" = 100° 48'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.94 }{ 19.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 35° 17'46" } = 8.65 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 17**2 - 10**2 } }{ 2 } = 13.838 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 10**2 - 12**2 } }{ 2 } = 12.59 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 10**2 - 17**2 } }{ 2 } = 7.053 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.