Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 6   b = 28   c = 28

Area: T = 83.51664654425
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 12.30112796559° = 12°18'5″ = 0.21546978322 rad
Angle ∠ B = β = 83.84993601721° = 83°50'58″ = 1.46334474107 rad
Angle ∠ C = γ = 83.84993601721° = 83°50'58″ = 1.46334474107 rad

Height: ha = 27.83988218142
Height: hb = 5.96554618173
Height: hc = 5.96554618173

Median: ma = 27.83988218142
Median: mb = 14.62987388383
Median: mc = 14.62987388383

Inradius: r = 2.69440795304
Circumradius: R = 14.08110556789

Vertex coordinates: A[28; 0] B[0; 0] C[0.64328571429; 5.96554618173]
Centroid: CG[9.54876190476; 1.98884872724]
Coordinates of the circumscribed circle: U[14; 1.5098684537]
Coordinates of the inscribed circle: I[3; 2.69440795304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6998720344° = 167°41'55″ = 0.21546978322 rad
∠ B' = β' = 96.15106398279° = 96°9'2″ = 1.46334474107 rad
∠ C' = γ' = 96.15106398279° = 96°9'2″ = 1.46334474107 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 = 6+28+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-6)(31-28)(31-28) } ; ; T = sqrt{ 6975 } = 83.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.52 }{ 6 } = 27.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.52 }{ 28 } = 5.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.52 }{ 28 } = 5.97 ; ;

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{ 28**2+28**2-6**2 }{ 2 * 28 * 28 } ) = 12° 18'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+28**2-28**2 }{ 2 * 6 * 28 } ) = 83° 50'58" ; ; gamma = 180° - alpha - beta = 180° - 12° 18'5" - 83° 50'58" = 83° 50'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.52 }{ 31 } = 2.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 12° 18'5" } = 14.08 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 6**2 } }{ 2 } = 27.839 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 6**2 - 28**2 } }{ 2 } = 14.629 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 6**2 - 28**2 } }{ 2 } = 14.629 ; ;
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.