Triangle calculator

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

You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 35   b = 35   c = 35

Area: T = 530.4410559818
Perimeter: p = 105
Semiperimeter: s = 52.5

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 30.31108891325
Height: hb = 30.31108891325
Height: hc = 30.31108891325

Median: ma = 30.31108891325
Median: mb = 30.31108891325
Median: mc = 30.31108891325

Inradius: r = 10.10436297108
Circumradius: R = 20.20772594216

Vertex coordinates: A[35; 0] B[0; 0] C[17.5; 30.31108891325]
Centroid: CG[17.5; 10.10436297108]
Coordinates of the circumscribed circle: U[17.5; 10.10436297108]
Coordinates of the inscribed circle: I[17.5; 10.10436297108]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c (as equilateral triangle).

a = 35 ; ; b = 35 ; ; c = 35 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 35 ; ; b = 35 ; ; c = 35 ; ; : Nr. 1

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

p = a+b+c = 35+35+35 = 105 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 105 }{ 2 } = 52.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.5 * (52.5-35)(52.5-35)(52.5-35) } ; ; T = sqrt{ 281367.19 } = 530.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 530.44 }{ 35 } = 30.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 530.44 }{ 35 } = 30.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 530.44 }{ 35 } = 30.31 ; ;

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{ 35**2+35**2-35**2 }{ 2 * 35 * 35 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+35**2-35**2 }{ 2 * 35 * 35 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 530.44 }{ 52.5 } = 10.1 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 60° } = 20.21 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 35**2 - 35**2 } }{ 2 } = 30.311 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 35**2 - 35**2 } }{ 2 } = 30.311 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 35**2 - 35**2 } }{ 2 } = 30.311 ; ;
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