Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 6.5   b = 6.5   c = 10.5

Area: T = 20.12202440032
Perimeter: p = 23.5
Semiperimeter: s = 11.75

Angle ∠ A = α = 36.12989274719° = 36°7'44″ = 0.63105687396 rad
Angle ∠ B = β = 36.12989274719° = 36°7'44″ = 0.63105687396 rad
Angle ∠ C = γ = 107.7422145056° = 107°44'32″ = 1.88804551744 rad

Height: ha = 6.19108443087
Height: hb = 6.19108443087
Height: hc = 3.83224274292

Median: ma = 8.10547825387
Median: mb = 8.10547825387
Median: mc = 3.83224274292

Inradius: r = 1.71223611918
Circumradius: R = 5.51221722173

Vertex coordinates: A[10.5; 0] B[0; 0] C[5.25; 3.83224274292]
Centroid: CG[5.25; 1.27774758097]
Coordinates of the circumscribed circle: U[5.25; -1.68797447881]
Coordinates of the inscribed circle: I[5.25; 1.71223611918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.8711072528° = 143°52'16″ = 0.63105687396 rad
∠ B' = β' = 143.8711072528° = 143°52'16″ = 0.63105687396 rad
∠ C' = γ' = 72.25878549439° = 72°15'28″ = 1.88804551744 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 6.5 ; ; b = 6.5 ; ; c = 10.5 ; ;

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

p = a+b+c = 6.5+6.5+10.5 = 23.5 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.5 }{ 2 } = 11.75 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.75 * (11.75-6.5)(11.75-6.5)(11.75-10.5) } ; ; T = sqrt{ 404.82 } = 20.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.12 }{ 6.5 } = 6.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.12 }{ 6.5 } = 6.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.12 }{ 10.5 } = 3.83 ; ;

6. 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{ 6.5**2+10.5**2-6.5**2 }{ 2 * 6.5 * 10.5 } ) = 36° 7'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.5**2+10.5**2-6.5**2 }{ 2 * 6.5 * 10.5 } ) = 36° 7'44" ; ;
 gamma = 180° - alpha - beta = 180° - 36° 7'44" - 36° 7'44" = 107° 44'32" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.12 }{ 11.75 } = 1.71 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.5 }{ 2 * sin 36° 7'44" } = 5.51 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 10.5**2 - 6.5**2 } }{ 2 } = 8.105 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.5**2+2 * 6.5**2 - 6.5**2 } }{ 2 } = 8.105 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 6.5**2 - 10.5**2 } }{ 2 } = 3.832 ; ;
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