Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 5.36   b = 5.36   c = 6.3

Area: T = 13.66106533427
Perimeter: p = 17.02
Semiperimeter: s = 8.51

Angle ∠ A = α = 54.0076988717° = 54°25″ = 0.94325997722 rad
Angle ∠ B = β = 54.0076988717° = 54°25″ = 0.94325997722 rad
Angle ∠ C = γ = 71.9866022566° = 71°59'10″ = 1.25663931092 rad

Height: ha = 5.097725871
Height: hb = 5.097725871
Height: hc = 4.33767153469

Median: ma = 5.19987883204
Median: mb = 5.19987883204
Median: mc = 4.33767153469

Inradius: r = 1.60552471613
Circumradius: R = 3.31223686594

Vertex coordinates: A[6.3; 0] B[0; 0] C[3.15; 4.33767153469]
Centroid: CG[3.15; 1.44655717823]
Coordinates of the circumscribed circle: U[3.15; 1.02443466874]
Coordinates of the inscribed circle: I[3.15; 1.60552471613]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.9933011283° = 125°59'35″ = 0.94325997722 rad
∠ B' = β' = 125.9933011283° = 125°59'35″ = 0.94325997722 rad
∠ C' = γ' = 108.0143977434° = 108°50″ = 1.25663931092 rad

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How did we calculate this triangle?

a = 5.36 ; ; b = 5.36 ; ; c = 6.3 ; ;

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

p = a+b+c = 5.36+5.36+6.3 = 17.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.02 }{ 2 } = 8.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.51 * (8.51-5.36)(8.51-5.36)(8.51-6.3) } ; ; T = sqrt{ 186.61 } = 13.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.66 }{ 5.36 } = 5.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.66 }{ 5.36 } = 5.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.66 }{ 6.3 } = 4.34 ; ;

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{ 5.36**2+6.3**2-5.36**2 }{ 2 * 5.36 * 6.3 } ) = 54° 25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.36**2+6.3**2-5.36**2 }{ 2 * 5.36 * 6.3 } ) = 54° 25" ; ; gamma = 180° - alpha - beta = 180° - 54° 25" - 54° 25" = 71° 59'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.66 }{ 8.51 } = 1.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.36 }{ 2 * sin 54° 25" } = 3.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.36**2+2 * 6.3**2 - 5.36**2 } }{ 2 } = 5.199 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.3**2+2 * 5.36**2 - 5.36**2 } }{ 2 } = 5.199 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.36**2+2 * 5.36**2 - 6.3**2 } }{ 2 } = 4.337 ; ;
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