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 = 624.3   b = 624.3   c = 318

Area: T = 95990.38106467
Perimeter: p = 1566.6
Semiperimeter: s = 783.3

Angle ∠ A = α = 75.2455064608° = 75°14'42″ = 1.31332741233 rad
Angle ∠ B = β = 75.2455064608° = 75°14'42″ = 1.31332741233 rad
Angle ∠ C = γ = 29.51098707841° = 29°30'36″ = 0.5155044407 rad

Height: ha = 307.5143633339
Height: hb = 307.5143633339
Height: hc = 603.7133085828

Median: ma = 384.7077190601
Median: mb = 384.7077190601
Median: mc = 603.7133085828

Inradius: r = 122.5466126193
Circumradius: R = 322.7944469053

Vertex coordinates: A[318; 0] B[0; 0] C[159; 603.7133085828]
Centroid: CG[159; 201.2387695276]
Coordinates of the circumscribed circle: U[159; 280.9198616775]
Coordinates of the inscribed circle: I[159; 122.5466126193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 104.7554935392° = 104°45'18″ = 1.31332741233 rad
∠ B' = β' = 104.7554935392° = 104°45'18″ = 1.31332741233 rad
∠ C' = γ' = 150.4990129216° = 150°29'24″ = 0.5155044407 rad

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How did we calculate this triangle?

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

a = 624.3 ; ; b = 624.3 ; ; c = 318 ; ;


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 = 624.3 ; ; b = 624.3 ; ; c = 318 ; ; : Nr. 1

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

p = a+b+c = 624.3+624.3+318 = 1566.6 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1566.6 }{ 2 } = 783.3 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 783.3 * (783.3-624.3)(783.3-624.3)(783.3-318) } ; ; T = sqrt{ 9214153176.69 } = 95990.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95990.38 }{ 624.3 } = 307.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95990.38 }{ 624.3 } = 307.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95990.38 }{ 318 } = 603.71 ; ;

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{ 624.3**2+318**2-624.3**2 }{ 2 * 624.3 * 318 } ) = 75° 14'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 624.3**2+318**2-624.3**2 }{ 2 * 624.3 * 318 } ) = 75° 14'42" ; ; gamma = 180° - alpha - beta = 180° - 75° 14'42" - 75° 14'42" = 29° 30'36" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95990.38 }{ 783.3 } = 122.55 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 624.3 }{ 2 * sin 75° 14'42" } = 322.79 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 624.3**2+2 * 318**2 - 624.3**2 } }{ 2 } = 384.707 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 318**2+2 * 624.3**2 - 624.3**2 } }{ 2 } = 384.707 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 624.3**2+2 * 624.3**2 - 318**2 } }{ 2 } = 603.713 ; ;
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