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 = 164   b = 164   c = 200

Area: T = 12998.46114474
Perimeter: p = 528
Semiperimeter: s = 264

Angle ∠ A = α = 52.42881306803° = 52°25'41″ = 0.9155043501 rad
Angle ∠ B = β = 52.42881306803° = 52°25'41″ = 0.9155043501 rad
Angle ∠ C = γ = 75.14437386394° = 75°8'37″ = 1.31215056515 rad

Height: ha = 158.5187822529
Height: hb = 158.5187822529
Height: hc = 129.9854614474

Median: ma = 163.4754768695
Median: mb = 163.4754768695
Median: mc = 129.9854614474

Inradius: r = 49.23765963917
Circumradius: R = 103.4588398168

Vertex coordinates: A[200; 0] B[0; 0] C[100; 129.9854614474]
Centroid: CG[100; 43.32882048247]
Coordinates of the circumscribed circle: U[100; 26.5266216306]
Coordinates of the inscribed circle: I[100; 49.23765963917]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.572186932° = 127°34'19″ = 0.9155043501 rad
∠ B' = β' = 127.572186932° = 127°34'19″ = 0.9155043501 rad
∠ C' = γ' = 104.8566261361° = 104°51'23″ = 1.31215056515 rad

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How did we calculate this triangle?

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

a = 164 ; ; b = 164 ; ; c = 200 ; ;

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

p = a+b+c = 164+164+200 = 528 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 528 }{ 2 } = 264 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 264 * (264-164)(264-164)(264-200) } ; ; T = sqrt{ 168960000 } = 12998.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12998.46 }{ 164 } = 158.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12998.46 }{ 164 } = 158.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12998.46 }{ 200 } = 129.98 ; ;

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{ 164**2+200**2-164**2 }{ 2 * 164 * 200 } ) = 52° 25'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 164**2+200**2-164**2 }{ 2 * 164 * 200 } ) = 52° 25'41" ; ; gamma = 180° - alpha - beta = 180° - 52° 25'41" - 52° 25'41" = 75° 8'37" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12998.46 }{ 264 } = 49.24 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 164 }{ 2 * sin 52° 25'41" } = 103.46 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 164**2+2 * 200**2 - 164**2 } }{ 2 } = 163.475 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 164**2 - 164**2 } }{ 2 } = 163.475 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 164**2+2 * 164**2 - 200**2 } }{ 2 } = 129.985 ; ;
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