Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 24.25   b = 48.5   c = 42

Area: T = 509.2549997843
Perimeter: p = 114.75
Semiperimeter: s = 57.375

Angle ∠ A = α = 309.9999998599° = 30° = 0.52435987732 rad
Angle ∠ B = β = 90.0055273912° = 90°19″ = 1.57108883739 rad
Angle ∠ C = γ = 59.99547262282° = 59°59'41″ = 1.04771055065 rad

Height: ha = 421.9999998221
Height: hb = 210.999999911
Height: hc = 24.25499998973

Median: ma = 43.71662369721
Median: mb = 24.24880669333
Median: mc = 32.08804652398

Inradius: r = 8.87658169559
Circumradius: R = 24.25500001027

Vertex coordinates: A[42; 0] B[0; 0] C[-0.00222321429; 24.25499998973]
Centroid: CG[13.99992559524; 8.08333332991]
Coordinates of the circumscribed circle: U[21; 12.12769330411]
Coordinates of the inscribed circle: I[8.875; 8.87658169559]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1500.00000014° = 150° = 0.52435987732 rad
∠ B' = β' = 89.9954726088° = 89°59'41″ = 1.57108883739 rad
∠ C' = γ' = 120.0055273772° = 120°19″ = 1.04771055065 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 = 24.25+48.5+42 = 114.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 114.75 }{ 2 } = 57.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.38 * (57.38-24.25)(57.38-48.5)(57.38-42) } ; ; T = sqrt{ 259335.56 } = 509.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 509.25 }{ 24.25 } = 42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 509.25 }{ 48.5 } = 21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 509.25 }{ 42 } = 24.25 ; ;

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{ 48.5**2+42**2-24.25**2 }{ 2 * 48.5 * 42 } ) = 30° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.25**2+42**2-48.5**2 }{ 2 * 24.25 * 42 } ) = 90° 19" ; ; gamma = 180° - alpha - beta = 180° - 30° - 90° 19" = 59° 59'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 509.25 }{ 57.38 } = 8.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.25 }{ 2 * sin 30° } = 24.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.5**2+2 * 42**2 - 24.25**2 } }{ 2 } = 43.716 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 24.25**2 - 48.5**2 } }{ 2 } = 24.248 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.5**2+2 * 24.25**2 - 42**2 } }{ 2 } = 32.08 ; ;
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