Triangle calculator

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: h_a = 95.01326618817
Height: h_b = 56.6243707586
Height: h_c = 56.05774705102

Median: m_a = 95.02876275617
Median: m_b = 65.5
Median: m_c = 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

Calculate another triangle

How did we calculate this triangle?

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.

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

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

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

2. Semiperimeter of the triangle

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

3. The triangle area using Heron's formula

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

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

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

5. Calculation of the inner angles of the triangle using a Law of Cosines

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

6. Inradius

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

7. Circumradius

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

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