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 = 59   b = 99   c = 100

Area: T = 2802.874352551
Perimeter: p = 258
Semiperimeter: s = 129

Angle ∠ A = α = 34.48882402335° = 34°29'18″ = 0.60219333453 rad
Angle ∠ B = β = 71.82883757221° = 71°49'42″ = 1.25436416527 rad
Angle ∠ C = γ = 73.68333840444° = 73°41' = 1.28660176556 rad

Height: ha = 95.01326618817
Height: hb = 56.6243707586
Height: hc = 56.05774705102

Median: ma = 95.02876275617
Median: mb = 65.5
Median: mc = 64.35106021728

Inradius: r = 21.72877017481
Circumradius: R = 52.09883193394

Vertex coordinates: A[100; 0] B[0; 0] C[18.4; 56.05774705102]
Centroid: CG[39.46766666667; 18.68658235034]
Coordinates of the circumscribed circle: U[50; 14.63767646013]
Coordinates of the inscribed circle: I[30; 21.72877017481]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5121759767° = 145°30'42″ = 0.60219333453 rad
∠ B' = β' = 108.1721624278° = 108°10'18″ = 1.25436416527 rad
∠ C' = γ' = 106.3176615956° = 106°19' = 1.28660176556 rad

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How did we calculate this triangle?

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

a = 59 ; ; b = 99 ; ; c = 100 ; ;


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 = 59 ; ; b = 99 ; ; c = 100 ; ; : Nr. 1

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

p = a+b+c = 59+99+100 = 258 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 258 }{ 2 } = 129 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 129 * (129-59)(129-99)(129-100) } ; ; T = sqrt{ 7856100 } = 2802.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2802.87 }{ 59 } = 95.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2802.87 }{ 99 } = 56.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2802.87 }{ 100 } = 56.06 ; ;

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{ 99**2+100**2-59**2 }{ 2 * 99 * 100 } ) = 34° 29'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 59**2+100**2-99**2 }{ 2 * 59 * 100 } ) = 71° 49'42" ; ; gamma = 180° - alpha - beta = 180° - 34° 29'18" - 71° 49'42" = 73° 41' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2802.87 }{ 129 } = 21.73 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 59 }{ 2 * sin 34° 29'18" } = 52.1 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 99**2+2 * 100**2 - 59**2 } }{ 2 } = 95.028 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 59**2 - 99**2 } }{ 2 } = 65.5 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 99**2+2 * 59**2 - 100**2 } }{ 2 } = 64.351 ; ;
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