Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 55   b = 55   c = 62

Area: T = 1408.369926976
Perimeter: p = 172
Semiperimeter: s = 86

Angle ∠ A = α = 55.69223485442° = 55°41'32″ = 0.97220148503 rad
Angle ∠ B = β = 55.69223485442° = 55°41'32″ = 0.97220148503 rad
Angle ∠ C = γ = 68.61553029116° = 68°36'55″ = 1.19875629531 rad

Height: ha = 51.21334279912
Height: hb = 51.21334279912
Height: hc = 45.43112667664

Median: ma = 51.75218115625
Median: mb = 51.75218115625
Median: mc = 45.43112667664

Inradius: r = 16.37663868577
Circumradius: R = 33.29220498954

Vertex coordinates: A[62; 0] B[0; 0] C[31; 45.43112667664]
Centroid: CG[31; 15.14437555888]
Coordinates of the circumscribed circle: U[31; 12.1399216871]
Coordinates of the inscribed circle: I[31; 16.37663868577]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.3087651456° = 124°18'28″ = 0.97220148503 rad
∠ B' = β' = 124.3087651456° = 124°18'28″ = 0.97220148503 rad
∠ C' = γ' = 111.3854697088° = 111°23'5″ = 1.19875629531 rad

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How did we calculate this triangle?

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

a = 55 ; ; b = 55 ; ; c = 62 ; ;

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

p = a+b+c = 55+55+62 = 172 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172 }{ 2 } = 86 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86 * (86-55)(86-55)(86-62) } ; ; T = sqrt{ 1983504 } = 1408.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1408.37 }{ 55 } = 51.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1408.37 }{ 55 } = 51.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1408.37 }{ 62 } = 45.43 ; ;

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{ 55**2+62**2-55**2 }{ 2 * 55 * 62 } ) = 55° 41'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 55**2+62**2-55**2 }{ 2 * 55 * 62 } ) = 55° 41'32" ; ; gamma = 180° - alpha - beta = 180° - 55° 41'32" - 55° 41'32" = 68° 36'55" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1408.37 }{ 86 } = 16.38 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 55 }{ 2 * sin 55° 41'32" } = 33.29 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 62**2 - 55**2 } }{ 2 } = 51.752 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 62**2+2 * 55**2 - 55**2 } }{ 2 } = 51.752 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 55**2 - 62**2 } }{ 2 } = 45.431 ; ;
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