Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10   b = 13   c = 13

Area: T = 60
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 45.24397298961° = 45°14'23″ = 0.79895822394 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 67.3880135052° = 67°22'49″ = 1.17660052071 rad

Height: ha = 12
Height: hb = 9.23107692308
Height: hc = 9.23107692308

Median: ma = 12
Median: mb = 9.60546863561
Median: mc = 9.60546863561

Inradius: r = 3.33333333333
Circumradius: R = 7.04216666667

Vertex coordinates: A[13; 0] B[0; 0] C[3.84661538462; 9.23107692308]
Centroid: CG[5.61553846154; 3.07769230769]
Coordinates of the circumscribed circle: U[6.5; 2.70883333333]
Coordinates of the inscribed circle: I[5; 3.33333333333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.7660270104° = 134°45'37″ = 0.79895822394 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 112.6219864948° = 112°37'11″ = 1.17660052071 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 = 10+13+13 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-10)(18-13)(18-13) } ; ; T = sqrt{ 3600 } = 60 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60 }{ 10 } = 12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60 }{ 13 } = 9.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60 }{ 13 } = 9.23 ; ;

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**2-10**2 }{ 2 * 13 * 13 } ) = 45° 14'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+13**2-13**2 }{ 2 * 10 * 13 } ) = 67° 22'49" ; ; gamma = 180° - alpha - beta = 180° - 45° 14'23" - 67° 22'49" = 67° 22'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60 }{ 18 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 45° 14'23" } = 7.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 13**2 - 10**2 } }{ 2 } = 12 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 10**2 - 13**2 } }{ 2 } = 9.605 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 10**2 - 13**2 } }{ 2 } = 9.605 ; ;
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