Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 12   b = 13   c = 13

Area: T = 69.1955375568
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 54.97328525008° = 54°58'22″ = 0.95994572754 rad
Angle ∠ B = β = 62.51435737496° = 62°30'49″ = 1.09110676891 rad
Angle ∠ C = γ = 62.51435737496° = 62°30'49″ = 1.09110676891 rad

Height: ha = 11.53325625947
Height: hb = 10.64554423951
Height: hc = 10.64554423951

Median: ma = 11.53325625947
Median: mb = 10.68987791632
Median: mc = 10.68987791632

Inradius: r = 3.6421861872
Circumradius: R = 7.32770792425

Vertex coordinates: A[13; 0] B[0; 0] C[5.53884615385; 10.64554423951]
Centroid: CG[6.17994871795; 3.54884807984]
Coordinates of the circumscribed circle: U[6.5; 3.38217288811]
Coordinates of the inscribed circle: I[6; 3.6421861872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0277147499° = 125°1'38″ = 0.95994572754 rad
∠ B' = β' = 117.486642625° = 117°29'11″ = 1.09110676891 rad
∠ C' = γ' = 117.486642625° = 117°29'11″ = 1.09110676891 rad

Calculate another triangle




How did we calculate this triangle?

a = 12 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 12+13+13 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-12)(19-13)(19-13) } ; ; T = sqrt{ 4788 } = 69.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.2 }{ 12 } = 11.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.2 }{ 13 } = 10.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.2 }{ 13 } = 10.65 ; ;

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{ 13**2+13**2-12**2 }{ 2 * 13 * 13 } ) = 54° 58'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12**2+13**2-13**2 }{ 2 * 12 * 13 } ) = 62° 30'49" ; ; gamma = 180° - alpha - beta = 180° - 54° 58'22" - 62° 30'49" = 62° 30'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.2 }{ 19 } = 3.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 54° 58'22" } = 7.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 13**2 - 12**2 } }{ 2 } = 11.533 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 12**2 - 13**2 } }{ 2 } = 10.689 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 12**2 - 13**2 } }{ 2 } = 10.689 ; ;
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.