Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 13   b = 26   c = 26

Area: T = 163.6343546377
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 25.17443917503
Height: hb = 12.58771958752
Height: hc = 12.58771958752

Median: ma = 25.17443917503
Median: mb = 15.92216833281
Median: mc = 15.92216833281

Inradius: r = 5.03548783501
Circumradius: R = 13.42663422669

Vertex coordinates: A[26; 0] B[0; 0] C[3.25; 12.58771958752]
Centroid: CG[9.75; 4.19657319584]
Coordinates of the circumscribed circle: U[13; 3.35765855667]
Coordinates of the inscribed circle: I[6.5; 5.03548783501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 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 = 13+26+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-13)(32.5-26)(32.5-26) } ; ; T = sqrt{ 26775.94 } = 163.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.63 }{ 13 } = 25.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.63 }{ 26 } = 12.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.63 }{ 26 } = 12.59 ; ;

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**2-13**2 }{ 2 * 26 * 26 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13**2+26**2-26**2 }{ 2 * 13 * 26 } ) = 75° 31'21" ; ; gamma = 180° - alpha - beta = 180° - 28° 57'18" - 75° 31'21" = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.63 }{ 32.5 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13 }{ 2 * sin 28° 57'18" } = 13.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 26**2 - 13**2 } }{ 2 } = 25.174 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 13**2 - 26**2 } }{ 2 } = 15.922 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 13**2 - 26**2 } }{ 2 } = 15.922 ; ;
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