Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 2   b = 23   c = 23

Area: T = 22.97882505862
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 4.9843812738° = 4°59'2″ = 0.08769839416 rad
Angle ∠ B = β = 87.5088093631° = 87°30'29″ = 1.5277304356 rad
Angle ∠ C = γ = 87.5088093631° = 87°30'29″ = 1.5277304356 rad

Height: ha = 22.97882505862
Height: hb = 1.99881087466
Height: hc = 1.99881087466

Median: ma = 22.97882505862
Median: mb = 11.58766302263
Median: mc = 11.58766302263

Inradius: r = 0.95774271078
Circumradius: R = 11.51108850001

Vertex coordinates: A[23; 0] B[0; 0] C[0.08769565217; 1.99881087466]
Centroid: CG[7.69656521739; 0.66660362489]
Coordinates of the circumscribed circle: U[11.5; 0.55004732609]
Coordinates of the inscribed circle: I[1; 0.95774271078]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.0166187262° = 175°58″ = 0.08769839416 rad
∠ B' = β' = 92.4921906369° = 92°29'31″ = 1.5277304356 rad
∠ C' = γ' = 92.4921906369° = 92°29'31″ = 1.5277304356 rad

Calculate another triangle




How did we calculate this triangle?

a = 2 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 2+23+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-2)(24-23)(24-23) } ; ; T = sqrt{ 528 } = 22.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.98 }{ 2 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.98 }{ 23 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.98 }{ 23 } = 2 ; ;

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{ 23**2+23**2-2**2 }{ 2 * 23 * 23 } ) = 4° 59'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2**2+23**2-23**2 }{ 2 * 2 * 23 } ) = 87° 30'29" ; ; gamma = 180° - alpha - beta = 180° - 4° 59'2" - 87° 30'29" = 87° 30'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.98 }{ 24 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2 }{ 2 * sin 4° 59'2" } = 11.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 23**2 - 2**2 } }{ 2 } = 22.978 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 2**2 - 23**2 } }{ 2 } = 11.587 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 2**2 - 23**2 } }{ 2 } = 11.587 ; ;
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.