Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 259   b = 147   c = 283

Area: T = 18914.67704224
Perimeter: p = 689
Semiperimeter: s = 344.5

Angle ∠ A = α = 65.41439307816° = 65°24'50″ = 1.14216884688 rad
Angle ∠ B = β = 31.07217017172° = 31°4'18″ = 0.54223034992 rad
Angle ∠ C = γ = 83.51443675012° = 83°30'52″ = 1.45876006856 rad

Height: ha = 146.0599231061
Height: hb = 257.3422454726
Height: hc = 133.673258249

Median: ma = 184.6044306559
Median: mb = 261.1188268223
Median: mc = 155.9587526269

Inradius: r = 54.90547036934
Circumradius: R = 142.4111402887

Vertex coordinates: A[283; 0] B[0; 0] C[221.8399222615; 133.673258249]
Centroid: CG[168.2879740872; 44.55875274968]
Coordinates of the circumscribed circle: U[141.5; 16.08659464218]
Coordinates of the inscribed circle: I[197.5; 54.90547036934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.5866069218° = 114°35'10″ = 1.14216884688 rad
∠ B' = β' = 148.9288298283° = 148°55'42″ = 0.54223034992 rad
∠ C' = γ' = 96.48656324988° = 96°29'8″ = 1.45876006856 rad

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How did we calculate this triangle?

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

a = 259 ; ; b = 147 ; ; c = 283 ; ;

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

p = a+b+c = 259+147+283 = 689 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 689 }{ 2 } = 344.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 344.5 * (344.5-259)(344.5-147)(344.5-283) } ; ; T = sqrt{ 357764757.19 } = 18914.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18914.67 }{ 259 } = 146.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18914.67 }{ 147 } = 257.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18914.67 }{ 283 } = 133.67 ; ;

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{ 147**2+283**2-259**2 }{ 2 * 147 * 283 } ) = 65° 24'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 259**2+283**2-147**2 }{ 2 * 259 * 283 } ) = 31° 4'18" ; ;
 gamma = 180° - alpha - beta = 180° - 65° 24'50" - 31° 4'18" = 83° 30'52" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18914.67 }{ 344.5 } = 54.9 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 259 }{ 2 * sin 65° 24'50" } = 142.41 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 147**2+2 * 283**2 - 259**2 } }{ 2 } = 184.604 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 283**2+2 * 259**2 - 147**2 } }{ 2 } = 261.118 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 147**2+2 * 259**2 - 283**2 } }{ 2 } = 155.958 ; ;
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