Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 30   b = 12.5   c = 32.5

Area: T = 187.5
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ B = β = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 12.5
Height: hb = 30
Height: hc = 11.53884615385

Median: ma = 19.52656241898
Median: mb = 30.64441266803
Median: mc = 16.25

Inradius: r = 5
Circumradius: R = 16.25

Vertex coordinates: A[32.5; 0] B[0; 0] C[27.69223076923; 11.53884615385]
Centroid: CG[20.06441025641; 3.84661538462]
Coordinates of the circumscribed circle: U[16.25; 0]
Coordinates of the inscribed circle: I[25; 5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ B' = β' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

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

p = a+b+c = 30+12.5+32.5 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-30)(37.5-12.5)(37.5-32.5) } ; ; T = sqrt{ 35156.25 } = 187.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 187.5 }{ 30 } = 12.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 187.5 }{ 12.5 } = 30 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 187.5 }{ 32.5 } = 11.54 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 12.5**2+32.5**2-30**2 }{ 2 * 12.5 * 32.5 } ) = 67° 22'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 30**2+32.5**2-12.5**2 }{ 2 * 30 * 32.5 } ) = 22° 37'11" ; ;
 gamma = 180° - alpha - beta = 180° - 67° 22'49" - 22° 37'11" = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 187.5 }{ 37.5 } = 5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 30 }{ 2 * sin 67° 22'49" } = 16.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 32.5**2 - 30**2 } }{ 2 } = 19.526 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32.5**2+2 * 30**2 - 12.5**2 } }{ 2 } = 30.644 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 30**2 - 32.5**2 } }{ 2 } = 16.25 ; ;
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