Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 60   b = 45   c = 69.15

Area: T = 1333.437735928
Perimeter: p = 174.15
Semiperimeter: s = 87.075

Angle ∠ A = α = 58.98551443667° = 58°59'7″ = 1.0299484979 rad
Angle ∠ B = β = 39.99990792909° = 39°59'57″ = 0.69881156314 rad
Angle ∠ C = γ = 81.01657763424° = 81°57″ = 1.41439920432 rad

Height: ha = 44.4487911976
Height: hb = 59.26438826347
Height: hc = 38.56765179835

Median: ma = 50.03436012096
Median: mb = 60.70109987562
Median: mc = 40.21328011335

Inradius: r = 15.31436647635
Circumradius: R = 35.00444564712

Vertex coordinates: A[69.15; 0] B[0; 0] C[45.96332863341; 38.56765179835]
Centroid: CG[38.37110954447; 12.85655059945]
Coordinates of the circumscribed circle: U[34.575; 5.46663834337]
Coordinates of the inscribed circle: I[42.075; 15.31436647635]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.0154855633° = 121°53″ = 1.0299484979 rad
∠ B' = β' = 140.0010920709° = 140°3″ = 0.69881156314 rad
∠ C' = γ' = 98.98442236576° = 98°59'3″ = 1.41439920432 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 = 60+45+69.15 = 174.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 174.15 }{ 2 } = 87.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 87.08 * (87.08-60)(87.08-45)(87.08-69.15) } ; ; T = sqrt{ 1778055.19 } = 1333.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1333.44 }{ 60 } = 44.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1333.44 }{ 45 } = 59.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1333.44 }{ 69.15 } = 38.57 ; ;

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{ 45**2+69.15**2-60**2 }{ 2 * 45 * 69.15 } ) = 58° 59'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60**2+69.15**2-45**2 }{ 2 * 60 * 69.15 } ) = 39° 59'57" ; ; gamma = 180° - alpha - beta = 180° - 58° 59'7" - 39° 59'57" = 81° 57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1333.44 }{ 87.08 } = 15.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 58° 59'7" } = 35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 69.15**2 - 60**2 } }{ 2 } = 50.034 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.15**2+2 * 60**2 - 45**2 } }{ 2 } = 60.701 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 60**2 - 69.15**2 } }{ 2 } = 40.213 ; ;
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