Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 18   b = 26   c = 26

Area: T = 219.5343596518
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 40.50444934844° = 40°30'16″ = 0.70769367732 rad
Angle ∠ B = β = 69.74877532578° = 69°44'52″ = 1.21773279402 rad
Angle ∠ C = γ = 69.74877532578° = 69°44'52″ = 1.21773279402 rad

Height: ha = 24.39326218353
Height: hb = 16.88771997321
Height: hc = 16.88771997321

Median: ma = 24.39326218353
Median: mb = 18.19334053987
Median: mc = 18.19334053987

Inradius: r = 6.27223884719
Circumradius: R = 13.85766490426

Vertex coordinates: A[26; 0] B[0; 0] C[6.23107692308; 16.88771997321]
Centroid: CG[10.74435897436; 5.62990665774]
Coordinates of the circumscribed circle: U[13; 4.79765323609]
Coordinates of the inscribed circle: I[9; 6.27223884719]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.4965506516° = 139°29'44″ = 0.70769367732 rad
∠ B' = β' = 110.2522246742° = 110°15'8″ = 1.21773279402 rad
∠ C' = γ' = 110.2522246742° = 110°15'8″ = 1.21773279402 rad

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How did we calculate this triangle?

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

p = a+b+c = 18+26+26 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-18)(35-26)(35-26) } ; ; T = sqrt{ 48195 } = 219.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 219.53 }{ 18 } = 24.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 219.53 }{ 26 } = 16.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 219.53 }{ 26 } = 16.89 ; ;

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{ 26**2+26**2-18**2 }{ 2 * 26 * 26 } ) = 40° 30'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+26**2-26**2 }{ 2 * 18 * 26 } ) = 69° 44'52" ; ;
 gamma = 180° - alpha - beta = 180° - 40° 30'16" - 69° 44'52" = 69° 44'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 219.53 }{ 35 } = 6.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 40° 30'16" } = 13.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 26**2 - 18**2 } }{ 2 } = 24.393 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 18**2 - 26**2 } }{ 2 } = 18.193 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 18**2 - 26**2 } }{ 2 } = 18.193 ; ;
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